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Climate Predictability Tool

Climate Predictability Tool. Simon Mason International Research Institute for Climate and Society The Earth Institute of Columbia University. What is CPT?. Climate Predictability Tool (CPT) is an easy-to-use Windows-based software package for making downscaled seasonal climate forecasts.

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Climate Predictability Tool

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  1. Climate Predictability Tool Simon Mason International Research Institute for Climate and Society The Earth Institute of Columbia University

  2. What is CPT? Climate Predictability Tool (CPT) is an easy-to-use Windows-based software package for making downscaled seasonal climate forecasts. It runs on Windows 95+. A source code version, which has no GUI or any of the graphics capabilities, is available for other platforms.

  3. What is CPT? Specifically, CPT is designed to produce statistical forecasts of seasonal climate using either the output from a GCM, or fields of sea-surface temperatures. The program provides extensive tests indicating forecast performance.

  4. What is CPT? • Downscaling – the translation of a forecast to a spatial and/or temporal resolution that is finer than that of the original forecast. statistical model coarse resolution fine resolution dynamical model

  5. What is CPT? Thus CPT is both a statistical prediction tool, and a statistical downscaling tool. Identical statistical techniques are used in both cases. When the predictors are outputs from another model, the procedure is called model output statistics (MOS), but conceptually there is no difference from a purely statistical forecast model.

  6. Why CPT?

  7. Why CPT? The national-based forecasts at the Climate Outlook Forums were made by regressing sea-surface temperatures onto rainfall:

  8. Why CPT? With over 16,000 grid boxes of SSTs, there is a very good chance of finding a strong correlation only by chance. With SSTs strongly correlated with temperatures in many different parts of the globe, there is a high chance of large errors in the regression parameters. The procedure did not allow adequately for probabilistic forecasts.

  9. Problems with Multiple Regression Multiplicity - Too many grids from which to choose. (For signifi- cance p-value of 0.10, for independent predictors) Multicolinearity - Predictors may be strongly correlated.

  10. Small sample problem Probabilities are sometimes obtained using contingency tables. These can be very unreliable when sample sizes are small.

  11. What CPT does • CPT addressed the problems by: • Being easy to learn and use. • Being designed to use gridded data (GCM output and SSTs) as predictors. • Using principal components (PCs, or EOFs) as predictors. • Performing rigorous cross-validation.

  12. Using PCA (or EOFs)? What are principal components (PCs), and why use them as predictors? Principal components are efficient summaries of large volumes of data. Given >16,000 grid boxes of SSTs on a 2º grid, it would be a lot easier if these could be reduced to a much smaller set. Principal components are an efficient way to reduce the data, since they involve minimal loss of information.

  13. Example of PCA (or EOFs) Example: Given set of exam scores of a group of 14 people, how can we best summarize the scores? One objective of summarizing the scores would be to distinguish the good students from the bad students. Principal components are ideal for obtaining such summaries, but they can also provide other informative summaries …

  14. Input Data for PCA (EOFs) Each subject is a variable (like one grid point), each person is a case, or sample (like one year).

  15. Loading weights (left), amplitudes (right) PC1 (or EOF1) – positive loadings on all exams. This distinguishes good from bad students (amplitudes are shown at right; good students have positive scores)

  16. Loading weights (left), amplitudes (right) PC2 (or EOF2) – oppositely signed loadings on physical vs. social sciences. This distinguishes physical scientists from social scientists (amplitudes are shown at right; physical scientists have positive score).

  17. PCA (or EOFs) in climate science First principal component (or EOF) of October – December 1950 -1999 sea-surface temperatures.

  18. PCA (or EOFs) in climate science: Principal Component Regression (PCR) • When using principal components of sea-surface temperatures the components have desirable features when doing a multiple regression: • They explain maximum amounts of variance, and therefore are representative of substantial sea temperature variability over large areas; • They are uncorrelated, so errors in estimating the regression parameters are smaller than if correlated. • Only a few PCs (or EOFs) need be retained, so the dangers of “fishing” are minimized.

  19. CCA With CCA, patterns (modes) of sea-surface temperatures can be predicted, using their modes from an earlier time, possibly in another ocean basin. These are superimposed (added together) to construct forecasts at individual locations. In CCA, not only is the predictor a whole field (multivariate), but the predictand also is. Or, patterns (modes) of rainfall over a land region are predicted, using modes of sea-surface temperature from an earlier time. CPT allows predictions to be made using either PCR or CCA.

  20. Canonical Correlation Analysis (CCA) July July (top) and December (bottom) tropical Pacific sea-surface tempera-ture anomaly, 1950-1999 December

  21. Analyses of correlation matrix of X and Y fields: 9 elements of X and Y x1 x2 x3 x4 x5 x6 x7 x8 x9y1 y2 y3 y4 y5 y6 y7 y8 y9 x1. | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - y1 | y2 | y3 | y4 | y5 | y6 | y7 | y8 | y9 | CCA ofXvsY EOFs of X Joint EOFs of X and Y CCA ofXvsY EOFs of Y

  22. Three Uses of CPT 1. To make a CCA forecast: Predictor is an observed field of a variable during an earlier time (e.g. Jul-Aug Pacific and Atlantic SST); target is a forecast of rainfall in a later season. • To make a CCA forecast: Predictor is a dynamical model prediction, target is a “corrected” forecast. • Make a principal components regression(PCR) forecast: predictors are PC amplitudes (usually from obs, but could be from model)

  23. We can use CCA to predict rainfall using the rainfall prediction of a dynamical model as the predictor (i.e., use #2 from previous slide). Why not just used model forecast as it is? Dynamical models often have systematic errors: bias in the mean bias in the amplitude bias in the shape of the anomaly pattern CCA can detect and correct such systematic errors, when trained on a history of model hindcasts and the corresponding observations

  24. Schematic showing two possible predictor designs in CCA 1. Observational predictor design X is observed earlier predictors, such as the field of governing SST Y is rainfall pattern prediction for a region of interest 2. Model MOS design X is dynamical model prediction of rainfall pattern around a region of interest 1. is a purely statistical forecast system 2. Is a dynamical forecast corrected by a statistical adjustment

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