Covariance Structure Analysis of Climate Model Outputs

Transcription

1 Covariance Structure Analysis of Climate Model Outputs Chintan Dalal* (Rutgers University) Doug Nychka (NCAR) Claudia Tebaldi (Climate Central) * Presenting poster

2 Goal

3 Goal Simulate computationally efficient projections of future climates.

4 Goal Simulate computationally efficient projections of future climates. % change in precipitation per degree of change in the global mean temperature Projection (2090) from the Community Earth System Modeling Group (NCAR) % change in precip per degree of global warming

5 Goal Simulate computationally efficient projections of future climates. % change in precipitation per degree of change in the global mean temperature Projection (2090) from the Community Earth System Modeling Group (NCAR) % change in precip per degree of global warming Earth system models running on a supercomputer take several months to output projections of future climates.

6 Challenges

7 Challenges Climate model outputs from various ESM groups can show plausible, yet different outcomes of future climates.

8 Challenges Climate model outputs from various ESM groups can show plausible, yet different outcomes of future climates. % change in precipitation per degree of change in the global mean temperature Model-MPI % change in precip per degree of global warming Projections (2090) from the CMIP5 ensemble.

9 Challenges Climate model outputs from various ESM groups can show plausible, yet different outcomes of future climates. % change in precipitation per degree of change in the global mean temperature Model-MPI Model-MRI % change in precip per degree of global warming Projections (2090) from the CMIP5 ensemble % change in precip per degree of global warming

10 Challenges Model-MRI Model-CCSM % change in precip per degree of global warming Model-MPI % change in precip per degree of global warming % change in precipitation per degree of change in the global mean temperature Climate model outputs from various ESM groups can show plausible, yet different outcomes of future climates. -20 Projections (2090) from the CMIP5 ensemble.

11 Statistical Emulator

12 Statistical Emulator Multivariate Normal Sampling (MVN) Scheme ỹ = µ + 1 2

13 Statistical Emulator Multivariate Normal Sampling (MVN) Scheme ỹ = µ NX ˆµ Multi-model ensemble mean, ˆµ = 1 N i=1 y i

14 Statistical Emulator Multivariate Normal Sampling (MVN) Scheme ỹ = µ NX ˆµ Multi-model ensemble mean, ˆµ = 1 N i=1 y i ˆ Covariance fitting, ( ) = {range, sill, nugget}

15 Challenges

16 Challenges Climate model outputs are not independent.

17 Challenges Climate model outputs are not independent. % change in precipitation per degree of change in the global mean temperature Model: NorESM1-M Projections (2090) from the same modeling group (NCC) in the CMIP5-RCP8.5 ensemble.

18 Challenges Climate model outputs are not independent. % change in precipitation per degree of change in the global mean temperature Model: NorESM1-M Model: NorESM1-ME Projections (2090) from the same modeling group (NCC) in the CMIP5-RCP8.5 ensemble.

19 Proposed Sampling Scheme

20 Proposed Sampling Scheme Weighted multi-model ensemble mean. ˆµ = nx j=1 m j X k=1 1 nm j y j,k, where n is the number of clusters.

21 Proposed Sampling Scheme Weighted multi-model ensemble mean. ˆµ = nx j=1 m j X k=1 1 nm j y j,k, where n is the number of clusters. Cluster similar climate model outputs NorESM1-M Modeling Team - MPI NorESM1-ME % change in precip per degree of global warming -20

22 Inter-model Comparison

23 Inter-model Comparison Compare models using a Riemannian metric between covariance matrices of climate model outputs.

24 Inter-model Comparison Compare models using a Riemannian metric between covariance matrices of climate model outputs. NorESM1-M Modeling Team - MPI ( 2 ) 30 Covariance 20 Fitting % change in precip per degree of global warming ( 1 ) ( 3 ) NorESM1-ME -20

25 Inter-model Comparison Compare models using a Riemannian metric between covariance matrices of climate model outputs. NorESM1-M Modeling Team - MPI ( 2 ) 30 Covariance 20 Fitting % change in precip per degree of global warming ( 1 ) ( 3 ) NorESM1-ME -20 ( i ) 2 Symmetric Postive Definite Matrices

26 Inter-model Comparison Compare models using a Riemannian metric between covariance matrices of climate model outputs. Manifold of Covariance Matrices NorESM1-M Modeling Team - MPI D( 1, 2 ) ( 2 ) 30 Covariance 20 Fitting % change in precip per degree of global warming ( 1 ) ( 3 ) NorESM1-ME -20 ( i ) 2 Symmetric Postive Definite Matrices

27 Inter-model Comparison Compare models using a Riemannian metric between covariance matrices of climate model outputs. Manifold of Covariance Matrices NorESM1-M Modeling Team - MPI D( 1, 2 ) ( 2 ) 30 Covariance 20 Fitting % change in precip per degree of global warming ( 1 ) ( 3 ) NorESM1-ME -20 ( i ) 2 Symmetric Postive Definite Matrices

28 Evaluation: Distance Matrix

29 Evaluation: Distance Matrix Euclidean distance between climate model outputs

30 Evaluation: Distance Matrix Euclidean distance between climate model outputs Geodesic distance between covariance matrices of climate model outputs

31 Evaluation: Distance Matrix Little Contrast Euclidean distance between climate model outputs Geodesic distance between covariance matrices of climate model outputs

32 Evaluation: Distance Matrix Little Contrast More Contrast More Dependencies Identified Less Bias in the Estimators Euclidean distance between climate model outputs Geodesic distance between covariance matrices of climate model outputs

33 Proposed Sampling Scheme

34 Proposed Sampling Scheme Manifold of Covariance Matrices j i % change in precip per degree of global warming Fitting covariance for each climate model output: CCSM4-20 Modeling Team - MPI - Mean % change in precip per degree of global warming N MRI

35 Proposed Sampling Scheme Sample a covariance matrix from a distribution on a manifold. ˆ N (, ( 1 ),..., ( N )) Manifold of Covariance Matrices j i % change in precip per degree of global warming Fitting covariance for each climate model output: CCSM4-20 Modeling Team - MPI - Mean % change in precip per degree of global warming N MRI

36 Evaluation: Semi-variogram Plots

37 Evaluation: Semi-variogram Plots Climate output models from the CMIP5-RCP2.6 ensemble Samples Spread (h), Semi-variogram function MVN Sampling Model: GFDL-ESM2G h, Distance in latitude/longitude units

38 Evaluation: Semi-variogram Plots Climate output models from the CMIP5-RCP2.6 ensemble Samples Spread (h), Semi-variogram function MVN Sampling Proposed Sampling Model: GFDL-ESM2G h, Distance in latitude/longitude units

39 Evaluation: Spatial Field

40 (h) Evaluation: Spatial Field Model: GFDL-ESM2G Proposed Sampling MVN Sampling h

41 (h) Evaluation: Spatial Field Model: GFDL-ESM2G Model: GFDL-ESM2G Proposed Sampling MVN Sampling h

42 Evaluation: Spatial Field Model: GFDL-ESM2G Model: GFDL-ESM2G (h) Proposed Sampling Proposed Sampling MVN Sampling h

43 Evaluation: Spatial Field Model: GFDL-ESM2G Model: GFDL-ESM2G (h) Proposed Sampling Proposed Sampling MVN Sampling h MVN Sampling

44 Evaluation: Spatial Field Model: GFDL-ESM2G Model: GFDL-ESM2G (h) Proposed Sampling Proposed Sampling MVN Sampling h MVN Sampling

45 Concluding Remarks

46 Concluding Remarks Analyzing the covariance matrix of climate model outputs on a manifold can potentially be used to investigate interdependencies in the CMIP5 ensembles.

47 Concluding Remarks Analyzing the covariance matrix of climate model outputs on a manifold can potentially be used to investigate interdependencies in the CMIP5 ensembles.

48 Concluding Remarks Analyzing the covariance matrix of climate model outputs on a manifold can potentially be used to investigate interdependencies in the CMIP5 ensembles. Proposed statistical emulator can potentially mimic the existing ensemble of climate model outputs.

49 Thank you!

50 Extra

51 Intuition Plot