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Data Analysis: Wheeler-Kiladis Space-Time Spectra

NCL version 5.1.0 is required to use the wkSpaceTime and wkSpaceTime_cam interfaces.

The scripts below are intended to be 'guide' to usage. They may work directly but, generally, the user will have to make some changes to the scripts.

The scripts are expecting data to be periodic (cyclic) in the longitude direction. The latitude extent must include latitudes about the equator. Further, the latitude and longitude coordinate arrays must consist of one dimensional monotonically {in/de}creasing values.

The following four libraries must be loaded prior to use.

load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/gsn_code.ncl"
load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/gsn_csm.ncl"
load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"
load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/diagnostics_cam.ncl"

*********************   REFERENCES  *********************
  Wheeler, M., G.N. Kiladis
     Convectively Coupled Equatorial Waves:
     Analysis of Clouds and Temperature in the
     Wavenumber-Frequency Domain
     J. Atmos. Sci., 1999,  56: 374-399.

   Hendon, H.H., and M.C. Wheeler 
     Some space-time spectral analyses
     of tropical convection and planetary-scale waves. 
     J. Atmos. Sci., 2008, 65: 2936-2948.

  Hayashi, Y.
     A Generalized Method of Resolving Disturbances into
     Progressive and Retrogressive Waves by Space and
     Fourier and TimeCross Spectral Analysis
     J. Meteor. Soc. Japan, 1971, 49: 125-128.
************ Space-Time Monitoring **************** Matt Wheeler (CAWCR: The Centre for Australian Weather and Climate Research) has a WWW link devoted to "real-time filtering of OLR data to monitor and predict the convective variations of the Madden-Julian oscillation and various convectively coupled equatorial waves."

Default Mode using the wkSpaceTime_cam interface.

wkSpaceTime_2.ncl: This illustrates using several of the options to change the default behavior. The data used were from ERA40 1999-2001 on a T85 grid. The original data were at a sampling rate of 4x per day (ie: every 6-hours). In this example The sampling rate was reduced (decimated) to 2x per day (ie: every 12 hours). This may be needed if memory is a problem.

Matt Wheeler commented on the spectral peaks in zonal wind (200 or 850hPa) for low westward-propagating wavenumbers (1-4) and periods in the range of about 4-6 days. (See the rightmost symmetric power figure.) "These are best described as resulting from global Rossby-Haurwitz waves. These are global and barotropic, and are not observable as peaks in the spectrum of OLR or precip. Despite the fact that they are not equatorially-trapped, their dispersion relation can be well-approximated by the same dispersion relation as used for the equatorially-trapped Rossby waves, provided the equivalent depth is set to ~10km, and you assume some global advecting basic state wind speed (~ 15 m/s). We discuss this more in the paper Hendon and Wheeler (2008, JAS - in press)."

wkSpaceTime_3.ncl: This illustrates using the direct interface, wkSpaceTime for calculations and plotting. The data used were from NCEP Reanalysis 2001-2005 on a 2.5x2.5 degree grid 4x per day. This is the interface that is most commonly used.

wkSpaceTime_4.ncl: This illustrates using addfiles to import a variable spanning multiple files. Here, *daily mean* TRMM data at 0.25 degree resolution and spanning the temporal period 2000-2009 are used.


Extract the Kelvin wave from the CLAUS outgoing long wave data.

Script and kf_filter donated by Carl Schreck [SUNY at Albany].