Presentation on theme: "Developing MADAv2 Using The Point-By-Point Regression Climate Field Reconstruction Method Edward R. Cook Tree-Ring Laboratory Lamont-Doherty Earth Observatory."— Presentation transcript:
Developing MADAv2 Using The Point-By-Point Regression Climate Field Reconstruction Method Edward R. Cook Tree-Ring Laboratory Lamont-Doherty Earth Observatory of Columbia University, New York 4 th Asia 2k Workshop Kyoto, Japan March 19-20, 2015
Reconstructing Asian Monsoon Climate Dynamics: MADAv1 A U.S. National Science Foundation sponsored project “Tree-Ring Reconstructions of Asian Monsoon Climate Dynamics” began in August, 2004 and is now finished. It resulted in the recently published paper in Science:
Patterned after the highly successful North American Drought Atlas (NADA; Cook and Krusic, 2004); Gridded drought reconstructed over Asian monsoon land areas; The Asian monsoon metric reconstructed: the monsoon season (JJA) Palmer Drought Severity Index (PDSI); The PDSI data source: Dai-Trenberth-Qian gridded data; The target field: June-July-August average PDSI on a 534 point 2.5° grid; The proxy data set: 327 annual tree-ring chronologies; The method of reconstruction: Ensemble Point-by-Point Regression (EPPR). The MADA
Some Reconstructed ‘Historical’ Droughts in Full Spatial Detail now from the MADA Lieberman, V. 2003. Strange Parallels: Southeast Asia in a Global Context, C. 800-1830, Vol. 1. Cambridge University Press, Cambridge. Shen et al. 2007. Exceptional drought events over eastern China during the last five centuries. Climatic Change 85:453-471. Davis. M. 2001. Late Victorian Holocausts: El Niño, Famines, and the Making of the Third World. Verso, London. Grove, R. 2007. The great El Niño of 1789-93 and its global consequences: reconstructing an extreme climate event in world environmental history. The Medieval History Journal 10:75-98. Dasuopu snow accumulation from Takata et al. 2009, PNAS
Proc Natl Acad Sci U S A. 2010 April 13; 107(15): 6748ñ6752.
Climate models say that explosive volcanism should produce drought in East and Southeast Asia. PDSI values derived from the millennium forced simulation of the NCAR CSM 1.4 [Ammann et al., 2007] and composited by the number of volcano key years indicated. But are they right? K.J. Anchukaitis, B.M. Buckley, E.R. Cook, B.I. Cook, R.D. D’Arrigo, C.M. Ammann. 2010. The influence of volcanic eruptions on the climate of the Asian monsoon region. Geophysical Research Letters, Vol. 37, L22703, doi:10.1029/2010GL044843.
The model results do not agree with the MADA, which suggests a deficiency in the NCAR CSM 1.4 model. WetWetWet DryDryDry MADA MODEL
Sequential fitting of single grid point principal component regression models over a grid. Grid point models are individually determined by overlapping sets of tree-ring chronologies located within a search radius that may be related to the correlation decay length (e-folding distance) of the climate field grid points. Tree-ring chronologies can be autoregressively modeled and screened for significance as candidate predictors of PDSI. They can also be lagged (e.g. t, t+1) w.r.t. climate. Nested reconstructions can be easily created to extend the reconstructions back in time and can vary in length over the domain as dictated by the tree-ring chronologies. Spatial climate variability in excess of the search radius used is preserved through the inherent spatial covariance structure between the grid points in the climate field itself. So what is Point-By-Point Regression?
PPR Originally Used Four levels of Variable Screening for Creating Each Grid Point Regression Model Level-1: An initial search radius around each grid point is used to locate candidate tree-ring chronologies - can dynamically expand if needed. Level-2: Only those tree-ring chronologies that correlate “significantly” with PDSI over the calibration period are retained as candidate predictors - a typical choice is the 90% 1- level. Level-3: After PCA of the retained Level-2 chronologies, retain only those PCs with eigenvalues>1.0 (Kaiser- Guttman Rule) as candidate predictors in PC regression - a priori and objective. Level-4: Enter the Level-3 orthogonal tree-ring PCs in stepwise regression by order of explanatory variance and use the minimum-AIC criterion to determine the final order of the regression model - a priori and objective.
From: Karl and Koscielny. 1982. Drought in the United States: 1895-1981. Journal of Climatology 2:313-329. 1 2 3 4 5 8 7 9 6 Rotated EOFs of Monthly PDSI based on Gridded Climate Division Data: 1895-1981
From: Cook et al. 1999. Drought Reconstructions for the continental United States. Journal of Climate 12:1145-1162 1 2 3 4 8 7 9 5 6 Rotated EOFs of Gridded Tree-Ring Reconstructed JJA PDSI Using PPR: 1700-1978
From: Cook et al. 1999. Drought Reconstructions for the continental United States. Journal of Climate 12:1145-1162 1 2 3 4 8 7 9 5 6 Rotated EOFs of Gridded Tree-Ring Reconstructed JJA PDSI Using PPR: 1700-1978 PPR has recovered the underlying spatial modes of variability of PDSI without being an explicit CFR method
Joint space-time methods? Canonical regression? Orthogonal spatial regression? SVD? RegEM? Potential problems here. No control over the grid point models: what tree-ring chronologies are used at each grid point, how they are used, and how each grid point model is fit. No control over the inclusion of potentially unstable long- range teleconnections across the domain by chance alone. Curse of dimensionality (frequently more variables than observations, potentially severe rank-deficiency). Reduced space (EOF) approaches to get around this “curse” will leave an EOF “fingerprint”on the spatial structure of the resulting reconstructions based in part on the EOF truncation chosen. The reconstructed field will be rank- deficient at the level of the EOF cutoff as well. So why not use joint space-time multivariate CFR methods instead of PPR?
Hard-rejection screening in original PPR (e.g. at the 90% level) has been eliminated now; It has been replaced by weighting each tree-ring chronology by some power of its correlation with each grid point of climate wTR = uTR r p where wTR is the weighted tree-ring series, uTR is the original unweighted tree-ring series in standard normal deviate form, r is the correlation between the tree-ring series and the climate variable of interest, and p is some power ≥0. Preserves rank order importance. Doing so perturbs the covariance matrix of the predictors that are subjected to PCA prior to use of tree-ring PCs in regression; This is typically done now for eight values of p: 0, 0.10, 0.25, 0.50, 0.67, 1.0, 1.5, and 2.0 to produce an ensemble of eight (8) members. The r p weighting for p>0 for a hard rejection r=0.26 (~90% level) ranges from 0.07 to 0.88. Ensemble Point-by-Point Regression (EPPR)
90% hard rejection used by Cook et al. (1999) found to be a “near- global optimum” has been eliminated now. Power-transformed correlations replace hard rejection with continuous weighting that ranges greatly over the span of powers (p>0) shown.
PPR can also easily estimate reconstruction uncertainties in two ways: classical parametric prediction intervals and semi-parametric intervals based on applying the maximum entropy bootstrap to the data. In either case, the form of the prediction intervals is the same (see Olive, 2007):
From: Cook, E.R., Palmer, J.G., Ahmed, M., Woodhouse, C.A., Fenwick, P., Zafar, M.U., Wahab, M. Khan, N. 2013. Five centuries of upper Indus River flow from tree rings. J. Hydrology 486:365–375. Indus River Discharge Reconstruction with Semi-Parametric Uncertainties
From: Cook, E.R., Palmer, J.G., Ahmed, M., Woodhouse, C.A., Fenwick, P., Zafar, M.U., Wahab, M. Khan, N. 2013. Five centuries of upper Indus River flow from tree rings. J. Hydrology 486:365–375. Uncertainties on Calibration/Validation Statistics are also possible using the Maximum Entropy Bootstrap procedure
Now on to the Monsoon Asia Drought Atlas, version 2 (MADAv2) -- not complete, in progress --
The Asian monsoon metric reconstructed: the monsoon season (JJA) self-calibrating Palmer Drought Severity Index (scPDSI); The scPDSI data source: Gerard van der Schrier gridded data for global land areas; The target field: June-July-August average scPDSI on a 2724 point 1.0° grid; The proxy data set: 453 annual tree-ring chronologies, from original MADAv1 and PAGES Asia2k project; The method of reconstruction: Ensemble Point-by-Point Regression (EPPR) – 8 values of p: 0, 0.10, 0.25, 0.50, 0.67, 1.0, 1.5, and 2.0 and 4 search radii: 1000, 1500, 2000, 2500 km – a total of 32 ensemble members. MADAv2
MADAv2 Calibration (1951-1989) and Validation Statistics (1920-1950)
MADAv2 DroughtsMADAv1 Droughts Preliminary Comparisons of Notable MADAv1 Droughts in MADAv2
Pederson/Hessl Mongol Pluvial: 1211-1225 CE Pederson, N., Hessl, A.E., Baatarbileg, N., Anchukaitis, K.J. and Cosmo, N.D. 2014. Pluvials, droughts, the Mongol Empire, and modern Mongolia. PNAS 111(12):4375-4379.
MADAv2 is nearing completion now. New tree-ring data are always wanted for inclusion in the network and there is still time for new records to be included. MADAv2 will be reported on at the AGU Chapman meeting "Evolution of the Asian Monsoon and Its Impact on Landscape, Environment and Society”, June 15-19th 2015, Hong Kong. It will also be an official PAGES Asia2k product, although by no means the only one on reconstructions of hydroclimatic variability over Asia. There is much more to do using other climate proxies and in integrating them into a more complete synthesis. A lot of challenges remain in that regard. Final Remarks