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Polar Amplification: Definitions, Interpretations and Problems Dmitry Dukhvoskoy Center for Ocean-Atmospheric Prediction Studies, Florida State University Andrey Proshutinsky Physical Oceanography research group, Woods Hole Oceanographic Institution James J. O’Brien Center for Ocean-Atmospheric Prediction Studies, Florida State University Steven L. Morey Center for Ocean-Atmospheric Prediction Studies, Florida State University Outline I. Overview of Polar Amplification phenomenon 1. Model-based definition: Amplification of a long-term variability 2. Observation-based (original) definition: Amplification of interannual variability II. Discussion on spatial averaging and Polar Amplification 1. Problems in Polar Amplification 2. Zonal averaging and bias in temporal variability of the estimates Two definitions of Polar Amplification Amplification of Amplification of Polar Amplification long-term short-term variability variability Results of GCM Statistical analysis of simulations of SAT under observations shows increased CO2 scenarios amplification with latitude reveal amplified warming of interannual variability in high latitudes (Manabe, of Northern hemispheric S., and R.J. Stouffer, 1980) SAT (Rubinstein, E.S., 1970) Polar Amplification in a GCM in Manabe and Stouffer (1980) in 4xCO2 Experiment Arctic region warming is larger and varies 14 16 with season 9 4 In low latitudes the 4 warming is small Latitude-time distribution of zonal mean difference in SAT (K) between the 4xCO2 and 1xCO2 experiment Mechanism of Polar Amplification in GCMs Positive ice-albedo feedback is a major reason of the warming amplification (Manabe and Stouffer, 1980; Lemke, 2001) Based on M. Holland website: www.asp.ucar.edu/colloquium/holland.html Problems in the Model-Based Definition: Sensitivity to Model Parameters 4 Normalized T increase 3 3 x Global Warming The increase in zonally averaged SAT for 2xCO2 conditions 2 2 x Global Warming as a function of latitude normalized by the globally averaged SAT 1 increase. 30 40 50 70 80 Latitude From Holland and Bitz, Climate Dyn., 21, 2003 Problems in the Model-Based Definition: Is it Supported by Observations? “Arctic and northern-hemispheric air-temperature trends during the 20th century are similar, … and do not support the predicted polar amplification of global warming.” Polyakov et al., J. Climate, 16, 2003 Northern hemispheric SAT trends (Jones et al., 1999) Trends, C/year Arctic and northern- Arctic SAT trends hemispheric SAT trends ranging from a 17 year (1985-2001) to the full record length (1875-2001), with 1 year increments Second Definition of Polar Amplification Polar Amplification is a phenomenon of poleward increase of interannual variability of zonal average of some meteorological characteristic (SAT, sea level pressure, precipitation, cloud cover) Zakharov, V.F., “Sea ice in the climate system”, 1996 Polar Amplification from Empirical Data Polar Amplification: the variability increases with latitude Standard deviations of zonal average SAT vs latitude for different months, 1898 - 1988 Based on Alekseev and Svyaschennikov (1991) Comparison of Two Definitions of Polar Amplification Common: • Based on zonal average of SAT • Describe amplification of a perturbation in high latitudes Different: • Time scales of variability • Origin of the data (simulated vs empirical) II. Problems in Polar Amplification Discussion on zonal averaging and temporal variabiltiy Problems in Zonal Averaging Approach 1. Different land-ocean distribution affects data variability and covariance structure S2 2. Different distances between neighboring grid points result in different covariance of the data Ratio of the areas: S1 S1/S2=cos1/cos2 4 Land-Sea Distribution in the Zonal Bands and Polar Amplification STD of zonal SAT Land/Sea Distribution in the bands Latitudes Latitudes Latitudes The SAT fields have been acquired from NOAA-CIRES Climate Diagnostic Center: www.cdc.noaa.gov for the period 1947-2003. The data have been detrended prior to any analysis. Spatial-Temporal Structure of the SAT Fields: Zero- lag Correlations for January in the Zonal Bands Artifact of small separation distance between the grid points 95% Significance Level Data separation distance (# of grid points) Spherical Grid with Normally Oriented Poles Annual SAT, 1948 Zonal SAT and its Variability Spherical Grid with Shifted Poles Annual SAT, 1948 Zonal SAT and its Variability Arctic S. America Australia Antarctic Amplification at the new poles Why is Covariance Structure Important in Zonal Averaging? Zonal Averaging 2 2 Z t 2 sin 2 sin 1 Z , , t cosdd ~ 1 0 1 For discrete data in a regular grid: k 2 Zi 2 * Z t ai zi t ~ i 1 1 ai * 2 * 1 sin sin * 2 * 1 1 * * 2 1* 2 sin 2 sin 1 Variance of Zonal Average k 1 Var Z ai a j Covzi , z j ai2Var ( zi ) 2 a a Covz , z k k k k ~ i j i j 1 1 i 1 i 1 j i 1 Zero-lag covariance between a pair of gridded data If a1 a2 ... ak 1 k k 1 Covz , z k k ~ 1 2 then Var Z 2 k i 1 Var ( zi ) 2 k i 1 j i 1 i j High covariance inflates the variance of the estimate Effect of Covariance on the Temporal Variability of an Average Three spatial-temporal data sets with the same variance (2=16) are generated with different covariance structure Zero-lag correlation X(1) Time x11 x1k X(2) Space X x xmk m1 X(3) Variance of space-averages ˆ ~ Var X (1) 1.1 Data separation distance ~ Var X ( 2 ) 0.66 ˆ The variance is inflated by covariance ~ Var X (3) 0.21 ˆ Sum of Covariances of Zonal SATs k 1 Covz , z k k ~ 1 2 Var Z 2 k i 1 Var ( zi ) 2 k i 1 j i 1 i j Latitudes Is the Polar Amplification Explained by Covariance? k 1 Covz , z k 2 k2 i j Variance of zonal SAT i 1 j i 1 Latitudes Latitudes Sum of Covariances –Correlation or Variability? For two random variables: Cov z1 , z 2 ( z1 , z 2 ) 1 2 Sum of covariances is a complex k 1 Covz , z ~ f , i , j k function of correlations of RVs i j i, j and their STDs: i 1 j i 1 k 1 Covz , z k How would this plot look if the 2 i j variance of SAT were the same? k2 i 1 j i 1 Pure Effect of Covariance on Variability of Zonal Average Sum of covariances for zonal SAT from the gridded data with equal variance Strongly decreased Equator Arctic Latitude s Adjusted Variance of Zonal SAT k 1 B 1 Covzi , z j k k Var Z 2 Var zi k 2 ~ 1 2 k 1 i 1 j i 1 k 1 i, j where B i j i k 1 80 i j i i, j Adjusted Variance Not-adjusted Variance Latitudes Latitudes Summary: Geophysical Aspect: * Phenomenon of Polar Amplification is strongly related to the land/sea distribution within the zonal bands. For the zones with large sea areas, the data are characterized by low interannual variability and strong spatial correlation Statistical Aspect: * Technique of zonal averaging introduces bias into estimates of temporal variability of the averages stemmed from covariance of the data * The bias results in a strongly decreased variance of the zonal average SAT in the regions 70N to 20N Correlograms of Zonal SAT C h h Corr X s , X s h C 0 C h j Nj X s X s h ˆ 1 i i Nj i 1 ( h) ˆ 95% Significance Level Data separation distance, h (km) First Definition of Polar Amplification In climate modeling studies: “… the Polar Amplification is viewed as the tendency for simulated temperature changes to be larger at high latitudes, as in the case of the warming induced by increased greenhouse gases” Glossary of Meteorology, amsglossary.allenpress.com/glossary