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!!!!!!!!!!!!! MJO Simulation Diagnostics - LEVEL 2 !!!!!!!!!!!!!!
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!!!!! DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT !!!!!
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! This is draft version of MSD calculation system.
! Please send feedback to kim@climate.snu.ac.kr
!  - Daehyun Kim
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! History
! [Created] Daehyun Kim - 25May2007
! [Revised] Daehyun Kim - 27Sep2007
! [Revised] Daehyun Kim - 21Apr2008
!  Include WK99, coherence squared and phase diagram
!  and MJO life cycle composite diagnostics
! [Revised] Daehyun Kim - 29Apr2008
!  Can be applied to the model which has 360 day calendar
!  leap.eq.2 => leap.eq.0 (in the c-shell script)

! Description
! This document contains descriptions for 
! the calculating & plotting system of level_2 MSD
! (MJO Simulation Diagnostics).

! Please visit
! http://climate.snu.ac.kr/mjo_metrics/index.htm
! to see the figures and detailed descriptions of level_2 MSD.

! The upper limit directory of this system is 'msd'.
! This document will give descriptions starting from this 
! directory. (e.g. msd/level_2/sample/ano/ano.sh)

! $var : {variable}_{source of data}
!  (e.g. olr_av, olr_cam, u850_snu)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
# Before the calculation & plotting

 Level 2 metrics calculation needs data from level 1 metrics.
 (e.g. daily anomaly data, daily filtered data)
 See msd/level_1/README_LEVEL_1 to know how to calculate them.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

1. Space-Time Power spectra

 * Order of calculations & plotting

 a. ano    :  go to Level 1 - 1.a

 b. zm2    :  meridionally averaging (10S-10N) raw and anomaly data

  Calculation :: msd/level_2/csh/zm2/zm2.sh
  Results     :: msd/level_1/$var/data/daily.10S10N.${period}.gdat
               ===> meridionally averaged (10S-10N) raw data
              :: msd/level_1/$var/data/daily.anom.10S10N.${period}.gdat
               ===> meridionally averaged (10S-10N) anomaly data

 c. stps    : calculate space-time power spectra

  * all season data
  Calculation :: msd/level_2/csh/stps/stps.all.sh
               ===> for all season data (with annual cycle)
  Results     :: msd/level_2/stps/all/$var/$var
               ===> space-time power spectra using all season data

  Plotting    :: msd/level_2/csh/stps/fig.all.sh
  Figures     :: msd/level_2/fig/stps/all/$var.all.gif

  * seasonally stratified data
  Calculation :: msd/level_2/csh/stps/stps.sea.sh
               ===> for seasonally stratified data (without annual cycle)
  Results     :: msd/level_2/stps/[win/sum]/$var/$var
               ===> space-time power spectra using seasonally stratified data

  Plotting    :: msd/level_2/csh/stps/fig.sea.sh
  Figures     :: msd/level_2/fig/stps/[win/sum]/$var.[win/sum].gif
 
 b. filter : filtering daily anomaly using Lanczos filter

  Calculation :: msd/level_1/csh/filter/filter.sh
  Results     :: msd/level_1/$var/data/daily.filt.20-100.lanz.100.period.gdat
               ===> 20-100 day filtered data using 201-points Lanczos filter
 
 c. var    : calculate variance using anomaly and filtered data

  Calculation :: msd/level_1/csh/var/var.sh
  Results     :: msd/level_1/$var/var/raw.[all/win/sum].gdat
              :: msd/level_1/$var/var/fil.[all/win/sum].gdat

  Plotting    :: msd/level_1/csh/var/fig.sh
  Figures     :: msd/level_1/fig/var/$var/all/*gif - all season
                 msd/level_1/fig/var/$var/sum/*gif - summer
                 msd/level_1/fig/var/$var/win/*gif - winter

2. Combined EOF

 * Order of calculations & plotting

 a. anom   : go to Level 1 1.a ===> for olr, u850, u200

 b. filter : go to Level 1 1.b ===> for olr, u850, u200

 c. zm3    : meridionally averaging (15S-15N) anomaly and filtered data
  Calculation :: msd/level_2/csh/zm3/zm3.sh
  Results     :: msd/level_1/$var/data/daily.anom.15S15N.${period}.gdat
               ===> meridionally averaged (15S-15N) anomaly data
              :: msd/level_1/$var/data/daily.filt.20-100.lanz.100.10S10N.${period}.gdat
               ===> meridionally averaged (15S-15N) filtered

 d. ceof   : Combined EOF

  Calculation :: msd/level_2/csh/ceof/ceof.sh
  Results     :: msd/level_2/$var/ceof/ceof.pct
               ===> percentage variance
              :: msd/level_2/$var/ceof/ceof.pct.gdat
               ===> used in percentage variance plotting
              :: msd/level_2/$var/ceof/ceof.var
               ===> percentage variance explained by each mode for each variable
              :: msd/level_2/$var/ceof/ceof.ev
               ===> eigen vectors
              :: msd/level_2/$var/ceof/ceof.ts
               ===> PC time series
              :: msd/level_2/$var/ceof/ceof.ts.pr
               ===> projcected PC time series

 e. sp256   : calculate power spectra using PCs
            : 183-day daily data is padded onto 256-day segment

  Calculation :: msd/level_2/csh/ceof/sp256.sh
  Results     :: msd/level_2/ceof/sp256.ts0[1/2]
               ===> power spectra from PC1 and PC2

 f. pcl     : calculate lead-lag correlation coefficients between
             PC1 and PC2 from 2.d

  Calculation :: msd/level_2/csh/ceof/pcl.sh
  Results     :: msd/level_2/ceof/pcl.llreg_2d.gdat
               ===> lag correlation coefficients

 g. crsp    : cross-spectra between PC1 and PC2 from CEOF

  Calculation :: msd/level_2/csh/ceof/crsp.sh
  Results     :: msd/level_2/ceof/crsp
               ===> coherence squared and phase between PC1 and PC2
              :: msd/level_2/ceof/crsp.moch
               ===> coherence squared averaged between 30-80 days period

  Plotting    :: msd/level_2/csh/ceof/fig.sh
  Figures     :: msd/level_2/fig/ceof/ceof.gif
               ===> eigen vectors
              :: msd/level_2/fig/ceof/pct.gif
               ===> percentage variance
              :: msd/level_2/fig/ceof/sp256.ts0[1/2].gif
               ===> power spectra using projected PCs
              :: msd/level_2/fig/ceof/pcl.gif
               ===> lag correlation between PC1 and PC2
              :: msd/level_2/fig/ceof/crsp.gif
               ===> coherence squared and phase between PC1 and PC2

3. MJO Life cycle composite

 * Order of calculations & plotting

 a. ceof    : go to Level 2 2. Combined EOF

 b. pre_comp: normalize PC 1/2 and determines amplitudes and phases
 
  Calculation :: msd/level_2/csh/comp/pre_comp.sh
  Results     :: msd/level_2/comp/data/amp_pha
               ===> amplitude and phase of normalized PC 1/2

 c. comp    : composite the 2d(lon.-lat.)/3d(lon.-pressure) fields

  Calculation :: msd/level_2/csh/comp/comp.sea.sh
  Results     :: msd/level_2/comp/$var/comp.[win/sum].gdat
               ===> composited data in 8 phases
                 msd/level_2/comp/$var/n_comp.[win/sum].gdat
               ===> number of days for each phases (for plotting)

  Plotting    :: msd/level_2/csh/comp/fig_2d.sea.sh
  Figures     :: msd/level_2/fig/comp/2d/comp.$var.[win/sum].gif
               ===> composited field (longitude-latitude)

  Plotting    :: msd/level_2/csh/comp/fig_2d.flux_with_olr.sea.sh
  Figures     :: msd/level_2/fig/comp/2d_olr/comp.$var.[win/sum].gif
               ===> composited field with contoured OLR (longitude-latitude)

  Plotting    :: msd/level_2/csh/comp/fig_wind.sea.sh
  Figures     :: msd/level_2/fig/comp/wind/comp.$var.[win/sum].gif
               ===> composited field with wind vectors (longitude-latitude)

  Plotting    :: msd/level_2/csh/comp/fig_3d.sea.sh
  Figures     :: msd/level_2/fig/comp/3d/comp.$var.[win/sum].gif
               ===> composited field (longitude-height)
                
4. Wheeler-Kiladis diagrams

 * Order of calculations & plotting

 a. anom   : go to Level 1 1.a ===> for olr, u850, u200

 b. seg    : make segments

  Calculation :: msd/level_2/csh/wk99/wk99_1_seg.sh
  Results     :: msd/level_2/wk99/$var/data/seg96_over60_[sym/asy].gdat
               ===> 96 days segments with 60 days overlab 
                   (symmetric/antisymmetric)

 c. power  : calculate power

  Calculation :: msd/level_2/csh/wk99/wk99_2_power.sh
  Results     :: msd/level_2/wk99/$var/power/power.[sym/asy].gdat
               ===> wavenumber-frequency power spectra 
                   (symmetric/antisymmetric)

 d. norm   : normalize the power

  Calculation :: msd/level_2/csh/wk99/wk99_3_norm.sh
  Results     :: msd/level_2/wk99/$var/power/norm.[sym/asy].gdat
               ===> normalized wavenumber-frequency power spectra 
                   (symmetric/antisymmetric)
  Results     :: msd/level_2/wk99/$var/power/back..gdat
               ===> background wavenumber-frequency power spectra

  Plotting    :: msd/level_2/csh/wk99/fig.sh
  Figures     :: msd/level_2/fig/wk99/wk99.$var.gif
               ===> normalized wavenumber-frequency power spectra
                   (symmetric/antisymmetric)

5. 2D cross spectra between OLR and wind fields

 * Order of calculations & plotting

 a. anom   : go to Level 1 1.a ===> for olr, u850, u200

 b. seg    : make segments

  Calculation :: msd/level_2/csh/coh2/coh2_1_seg.sh
  Results     :: msd/level_2/coh2/$var/data/seg256_over200_sym_asy.gdat
               ===> 256 days segments with 200 days overlab 
                   (symmetric/antisymmetric)

 c. power  : calculate power

  Calculation :: msd/level_2/csh/coh2/coh2_2_power.sh
  Results     :: msd/level_2/coh2/$var/power/power.[sym/asy].gdat
               ===> wavenumber-frequency power spectra and co-/quadrature-
                   spectra (symmetric/antisymmetric)

              :: msd/level_2/coh2/$var/power/coh2.[sym/asy].gdat
               ===> wavenumber-frequency coherence and phase between
                   OLR and wind fields (symmetric/antisymmetric)

  Plotting    :: msd/level_2/csh/coh2/fig.sh
  Figures     :: msd/level_2/fig/coh2/coh2.$var.gif
               ===> wavenumber-frequency coherence and phase between
                   OLR and wind fields (symmetric/antisymmetric)


! * Contact : Daehyun Kim (kim@climate.snu.ac.kr)

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!!! Last updated in 27Sep2007 by Daehyun Kim
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