Combining Physical and Statistical Models in Order to Narrow - - PowerPoint PPT Presentation

Patrick

• T. Brown

Carnegie Institution for Science, Stanford CA Stanford EE Computer Systems Colloquium January 17, 2018

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

1900 1950 2000 2050 2100

Year

• 1

1 2 3 4 5 6

Relative Global Temperature (C) a, pretty modeled and observed global temperature

Modeled Future RCP 2.6 Modeled Future RCP 4.5 Modeled Future RCP 6.0 Modeled Future RCP 8.5 Modeled Historical Observations

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

1900 1950 2000 2050 2100

Year

• 1

1 2 3 4 5 6

Relative Global Temperature (C) a, pretty modeled and observed global temperature

Modeled Future RCP 2.6 Modeled Future RCP 4.5 Modeled Future RCP 6.0 Modeled Future RCP 8.5 Modeled Historical Observations

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

1900 1950 2000 2050 2100

Year

• 1

1 2 3 4 5 6

Relative Global Temperature (C) a, pretty modeled and observed global temperature

Modeled Future RCP 2.6 Modeled Future RCP 4.5 Modeled Future RCP 6.0 Modeled Future RCP 8.5 Modeled Historical Observations

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

1900 1950 2000 2050 2100

Year

• 1

1 2 3 4 5 6

Relative Global Temperature (C) a, pretty modeled and observed global temperature

Modeled Future RCP 2.6 Modeled Future RCP 4.5 Modeled Future RCP 6.0 Modeled Future RCP 8.5 Modeled Historical Observations

+

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

1900 1950 2000 2050 2100

Year

• 1

1 2 3 4 5 6

Relative Global Temperature (C) a, pretty modeled and observed global temperature

Modeled Future RCP 2.6 Modeled Future RCP 4.5 Modeled Future RCP 6.0 Modeled Future RCP 8.5 Modeled Historical Observations

+

1900 1950 2000 2050 2100

Year

• 1

1 2 3 4 5 6

Relative Global Temperature (C) a, pretty modeled and observed global temperature

Modeled Future RCP 2.6 Modeled Future RCP 4.5 Modeled Future RCP 6.0 Modeled Future RCP 8.5 Modeled Historical Observations

“The Agreement aims to respond to the global climate change threat by keeping a global temperature rise this century well below 2 degrees Celsius above pre-industrial levels and to pursue efforts to limit the temperature increase even further to 1.5 degrees Celsius”

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

1900 1950 2000 2050 2100

Year

• 1

1 2 3 4 5 6

Relative Global Temperature (C) a, pretty modeled and observed global temperature

Modeled Future RCP 2.6 Modeled Future RCP 4.5 Modeled Future RCP 6.0 Modeled Future RCP 8.5 Modeled Historical Observations

Scenario Uncertainty Response Uncertainty

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases? Projections differ by a factor of 2

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Heat capacity (W yr m-2 K-1) Global Average Surface Temperature Perturbation (K) Net Energy Flux (W m-2)

Ocean Space Atmosphere

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

340 W/m2 76 W/m2 24 W/m2 240 W/m2 Net Energy Flux (W m-2)

Ocean Space Atmosphere

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

340 W/m2 76 W/m2 24 W/m2 240 W/m2 Net Energy Flux (W m-2)

Ocean Space Atmosphere

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

“Forcing” (W/m2) “Feedback” (W/m2) Climate Feedback Parameter (W m-2 K-1) 340 W/m2 76 W/m2 24 W/m2 240 W/m2

Ocean Space Atmosphere

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Climate Feedback Parameter (W m-2 K-1) 340 W/m2 76 W/m2 24 W/m2 240 W/m2

Ocean Space Atmosphere

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Small uncertainty for CO2 Large uncertainty Large uncertainty 340 W/m2 76 W/m2 24 W/m2 240 W/m2

Ocean Space Atmosphere

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

340 W/m2 76 W/m2 24 W/m2 240 W/m2

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #1: estimate F and ∆T

• ver some time in

the past

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

• Mathematical /

mechanistic models of the entire Earth system run on supercomputers

• Typically about a

million lines of code

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

• Developed

at many centers around the world

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

• Developed

at many centers around the world

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

• Developed

at many centers around the world

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

• Discretize the

Earth system in space and time

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

• Use laws of

physics to calculate state

• f Earth system

at every 3D location

• March forward

in time with time steps of ~30 minutes

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

• Number of

processes explicitly represented has increased over time

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

• Spatial

resolution has increased over time

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

• Spatial resolution not sufficient to

represent many important processes

• These processes must be

‘parameterized’

• Example: Cloud fraction
• Calculated based on a formula that

is only semi-physical and has tunable parameters that are poorly constrained

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

How much global warming should we expect for a given increase in the atmospheric concentration of greenhouse gases?

Strategy #2: Increase greenhouse gas concentrations in a physical climate model and have it calculate ∆T Physical Global Climate Models

• Most of uncertainty in future

warming comes from uncertainty in feedbacks (𝝻) that stems from important processes being ‘parameterized’

• The primary goal of our study

was to narrow this range of model uncertainty and to assess whether the upper or lower end of the range is more likely.

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

• We utilize the idea that the physical models that

are going to be the most skillful in their projections of future warming (and thus have the most accurate parameterizations) should also be the most skillful in other contexts like simulating the recent past.

• Emergent Constraints: If there is a

relationship between how physical models simulate the recent past and how much warming they simulate in the future, then we should be able to use this statistical relationship, along with

• bservations of the recent past, to statistically

narrow the range of future warming projections

Something you can observe currently (predictor)

Climate Models

“Emergent Constraints” Something you want to know but can’t observe (predictand)

Something you can observe currently (predictor)

Climate Models

“Emergent Constraints” Something you want to know but can’t observe (predictand)

Something you can observe currently (predictor)

Climate Models

“Emergent Constraints” Something you want to know but can’t observe (predictand)

Something you want to know but can’t observe (predictand)

Something you can observe currently (predictor)

Climate Models

“Emergent Constraints”

Observationally-informed central estimate

Outgoing Shortwave Radiation (OSR) Outgoing Longwave Radiation (OLR) N=ISR – OSR – OLR

What variables are most appropriate to use as predictors ?

Incoming Shortwave Radiation (ISR)

Outgoing Shortwave Radiation (OSR) Outgoing Longwave Radiation (OLR) N=ISR – OSR – OLR Mean climatology Magnitude of the seasonal cycle Magnitude of monthly variability 1 2 3 4 5 6 7 8 9 (Local average) (Local standard deviation of average seasonal cycle) (Local standard deviation monthly variability apart from seasonal cycle)

What variables are most appropriate to use as predictors ?

Outgoing Shortwave Radiation (OSR) Outgoing Longwave Radiation (OLR) N=ISR – OSR – OLR Mean climatology Magnitude of the seasonal cycle Magnitude of monthly variability CERES Satellite Record (2001-2015)

What variables are most appropriate to use as predictors ?

Outgoing Shortwave Radiation (OSR) Outgoing Longwave Radiation (OLR) N=ISR – OSR – OLR Mean climatology Magnitude of the seasonal cycle Magnitude of monthly variability 1 2 3 4 5 6 7 8 9

What variables are most appropriate to use as predictors ?

Outgoing Shortwave Radiation (OSR) Outgoing Longwave Radiation (OLR) N=ISR – OSR – OLR Mean climatology Magnitude of the seasonal cycle Magnitude of monthly variability

What variables are most appropriate to use as predictors ?

Outgoing Shortwave Radiation (OSR) Outgoing Longwave Radiation (OLR) N=ISR – OSR – OLR Mean climatology Magnitude of the seasonal cycle Magnitude of monthly variability

What method is appropriate to statistically relate the predictor to the predictand?

Outgoing Shortwave Radiation (OSR) Mean climatology (Predictor Variable, [x])

What method is appropriate to statistically relate the predictor to the predictand?

Mean climatology Outgoing Shortwave Radiation (OSR) 37 latitudes 36 models (Predictor Variable, [x]) (Predictand Variable, y) ∆T 2.0 3.2 4.4 2.1 2.6 3.6 3.2 2.2 4.8 3.9 3.0 3.3 36 models

What method is appropriate to statistically relate the predictor to the predictand?

What method is appropriate to statistically relate the predictor to the predictand?

Mean climatology Outgoing Shortwave Radiation (OSR) 37 latitudes 36 models (Predictor Variable, [x]) (Predictand Variable, y) ∆T 2.0 3.2 4.4 2.1 2.6 3.6 3.2 2.2 4.8 3.9 3.0 3.3

• There are many more predictors than

variables to predict

• But predictors themselves are

correlated with each other

• Relate Predictor Field to Predictand

using Partial Least Squares Regression (Wold, 1966) 36 models

(Predictand Variable, y) ∆T 2.0 3.2 4.4 2.1 2.6 3.6 3.2 2.2 4.8 3.9 3.0 3.3

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2664 Locations→ ← 36 Models

=

36 models

• Could think of this in terms of Multiple Linear Regression

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• Because of the high degree of spatial autocorrelation in the predictor fields used here, the columns in

[X] will be highly collinear, and thus [X] will be well below full rank.

• PLS creates a small number of ‘PLS components’ or ‘latent vectors’ that are:
• Linear combinations of the original original columns
• Uncorrelated with each other
• Explain as much of the variability in the predictand as possible

Partial Least Squares Regression

• System is underdetermined (more unknowns than equations)

(Predictand Variable, y) ∆T 2.0 3.2 4.4 2.1 2.6 3.6 3.2 2.2 4.8 3.9 3.0 3.3

=

36 models

• Could think of this in terms of Multiple Linear Regression
• Must guard against over-fitting
• PLS procedure is more than capable of overfitting predictors to predictands.
• We evaluated the predictive skill of the predictors (and thus the constrained

warming uncertainty) using leave-one-out cross-validation.

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Partial Least Squares Regression

∆T (predictand)

Linear combination of PLS components (predictor)

Cross-validation

Training Climate Models Test Climate Model

Training Climate Models Test Climate Model

Cross-validation ∆T (predictand)

Linear combination of PLS components (predictor)

Training Climate Models Test Climate Model

Cross-validation ∆T (predictand)

Linear combination of PLS components (predictor)

Training Climate Models Test Climate Model Error 1

Cross-validation ∆T (predictand)

Linear combination of PLS components (predictor)

Training Climate Models Test Climate Model Error 2

Cross-validation ∆T (predictand)

Linear combination of PLS components (predictor)

Training Climate Models Test Climate Model Error 3

Cross-validation ∆T (predictand)

Linear combination of PLS components (predictor)

Training Climate Models Test Climate Model Error 4

Cross-validation ∆T (predictand)

Linear combination of PLS components (predictor)

Training Climate Models Test Climate Model Error 5

Cross-validation

Results

∆T (predictand)

Linear combination of PLS components (predictor)

Training Climate Models

Cross-validation ∆T (predictand)

Linear combination of PLS components (predictor)

Training Climate Models Test Climate Model

Results

∆T (predictand)

Linear combination of PLS components (predictor)

Results

Observations of several diverse attributes of Earth’s global energy budget indicate both individually and collectively that global warming is likely to be greater than that suggested by the unconstrained model suite.

1960 1980 2000 2020 2040 2060 2080 2100

Year

1 2 3 4 5 6

GMSAT above preindustrial (C) RCP 8.5

Global average surface temperature above preindustrial (C) +2∘C above preindustrial

Results

1960 1980 2000 2020 2040 2060 2080 2100

Year

1 2 3 4 5 6

GMSAT above preindustrial (C) RCP 8.5

Raw climate model projections Historical climate model range Observations +2∘C above preindustrial Global average surface temperature above preindustrial (C)

Results

1960 1980 2000 2020 2040 2060 2080 2100

Year

1 2 3 4 5 6

GMSAT above preindustrial (C) RCP 8.5

Raw climate model projections Historical climate model range Observation s +2∘C above preindustrial Observationally- informed projections Global average surface temperature above preindustrial (C)

Results

1960 1980 2000 2020 2040 2060 2080 2100

Year

1 2 3 4 5 6

GMSAT above preindustrial (C) RCP 8.5

Raw climate model projections Historical climate model range Observation s +2∘C above preindustrial Observationally- informed projections Global average surface temperature above preindustrial (C)

• Our results suggest that

model shortcomings can likely be used to dismiss the least severe projections, rather than the most severe projections

Results

• It is sometimes argued

that climate model- projected global warming should be taken less seriously on the grounds that climate models are imperfect in their simulation of the current climate.

Outgoing Shortwave Radiation (OSR) Outgoing Longwave Radiation (OLR) N=ISR – OSR – OLR Mean climatology Magnitude of the seasonal cycle Magnitude of monthly variability 1 2 3 4 5 6 7 8 9

Results - Physical Mechanisms

Outgoing Shortwave Radiation (OSR) Outgoing Longwave Radiation (OLR) N=ISR – OSR – OLR Mean climatology Magnitude of the seasonal cycle Magnitude of monthly variability 1 2 3 4 5 6 7 8 9

Results - Physical Mechanisms

Outgoing Shortwave Radiation (OSR) Mean climatology

Results - Physical Mechanisms

Results

Outgoing Shortwave Radiation (OSR) Mean climatology 1 Positive = Models with more OSR in this location, warm more in the future Negative = Models with more OSR in this location, warm less in the future Contours = Satellite observations relative to model mean

• Models with more average reflected sunlight from clouds and sea ice over the the

southern ocean, warm more in the future

• More potential for positive shortwave sea-ice feedbacks
• Less potential for negative shortwave cloud feedbacks
• Observations tell us that models with more OSR are correct
• Physical Mechanisms

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming

Patrick

• T. Brown

Carnegie Institution for Science, Stanford CA Stanford EE Computer Systems Colloquium January 17, 2018

Combining Physical and Statistical Models in Order to Narrow Uncertainty in Projections of Global Warming