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Polar Amplification - DecVar_

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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=cos1/cos2  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  cosdd
~                                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 Covzi , z j    ai2Var ( zi )  2           a a Covz , 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

                                               Covz , 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

                                          Covz , 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

          Covz , 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

                                    Covz , z  ~ f                          , i , j 
                                          k
function of correlations of RVs                      i    j               i, j
and their STDs:                   i 1 j  i 1




                                                              k 1

                                                                Covz , 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 Covzi , 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 70N to 20N
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

								
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