Major Stratospheric Sudden Warmings

Introduction

This diagnostic calculates the frequency and timing of major mid-winter stratospheric sudden warmings, the basic unit of stratospheric variability. It builds on old diagnostics of SSWs first proposed by SCOSTEP in the 1960s. The work here is most directly related to two recent papers which established climatologies of SSWs in NCEP/NCAR and ERA-40 reanalysis datasets (Charlton and Polvani, 2007).

In addition to counting the number of SSWs, further diagnostics which characterise the dynamical structure of SSWs are included. An example of the application of both sets of diagnostics can be found in Charlton et al., 2007.

Calculation Description

Finding the central date of SSWs

The central date of SSWs is found by considering the time evolution of zonal mean zonal winds at 60N and 10hPa only. This data is required at daily time resolution between November and April of each winter season in the model.

• Define a holding array, H, of length equal to the number of days in your zonal mean zonal wind record.
• Find all days of zonal mean zonal winds less than 0 ms^-1 (easterly). Mark H with a 1 for each day with easterly winds.
• Scan through the data, the first time that winds become easterly is considered the preliminary central date, d, of an SSW. Preliminary central dates can be found by looking for zero to one changes in H. Mark days d+1 to d+20 with zeroes. This prevents double counting of SSW events.
• For each d, find all days with zonal mean zonal winds greater than or equal to 0 ms^-1 (westerly) between d and April 30th of the corresponding winter season. Count the largest number of consecutive days with westerly winds, if this number is less than 10 then do not count that event as an SSW and mark d with a zero. This step prevents counting of final warming events.
• H will now contain all central dates for SSWs in your model integration.

Estimate the frequency of SSWs per winter season

This plot shows an example of the comparison of the frequency of SSWs occuring in each winter month of the NCEP/NCAR reanalysis (open bars) with 6 GCM integrations (coloured bars).

Estimating the standard error of the SSW estimate

The standard error of the SSW estimate can be calculated as follows, which allows you to estimate if the number of SSWs is signifcantly different to the reanalysis data or another model.Refer to Appendix A of Charlton et al. (2007) for more details. Please follow the directions on the attached PDF to calculate the sample mean frequency of SSWs, the standard error and contruct a significance test of the frequency of SSWs in your GCM compared to the NCEP/NCAR reanalysis

Benchmark diagnostics of SSWs

Once the central SSW dates have been established the following diagnostics can be calculated for each SSW and a comparison made between the dynamics of SSWs in your model and the reanalysis data. Datasets containing estimates of each benchmark for SSWs in the reanalysis data are included on this page.

• Polar Cap Temperature Anomaly @ 10hPa (&Delta T₁₀)
  The area-weighted, mean, 10hPa polar-cap temperature anomaly, 90-50N, ± 5 days from the central date of each SSW.
• Polar Cap Temperature Anomaly @ 100hPa (&Delta T₁₀₀)
  The area-weighted, mean, 10hPa polar-cap temperature anomaly, 90-50N, ± 5 days from the central date of each SSW.
• Zonal Wind Deceleration @ 10hPa (&Delta U₁₀)
  The difference in mean zonal mean zonal wind at 60N and 10hPa, 15-5 days prior to the onset date minus 0-5 days after the central date.
• Heatflux @ 100hPa (&Delta [v'T']₁₀₀)
  The area-weighted, mean, 100hPa [v'T'] anomaly, 20-0 days before the central date. Here square brackets represent a zonal average and primes indicate a departure from the zonal average.

  In each case, first calculate a climatology of each diagnostic in your model and then calculate the anomaly from the climatology for the given time period. Summary statistics can be plotted as a box and whiskers plot

  This plot shows an example of the comparison of the distribution of a given benchmark, in this case &Delta T₁₀, also taken from Charlton et al. (2007). The clear box plot shows the benchmark for SSWs in NCEP/NCAR reanalysis data, the coloured box plots show the distribution in 6 different stratosphere resolving GCMs.
  

  postscript file

  Benchmark Data from Reanalysis

  SSW occurence dates and summary statistics

  
  SSW central dates in the NCEP/NCAR reanalysis are here
  SSW central dates in the ERA-40 reanalysis are here
  Summary statistics for these datasets are shown in the following table. All quoted quoted statistics are SSW events per year. Quoted standard error is for total frequency only and is derived using the proceedure outlined above.

  Dataset	SSW Frequency	Standard Error	Nov Freq.	Dec Freq.	Jan Freq.	Feb Freq.	Mar Freq.
  NCEP/NCAR	0.60	0.10	0.04	0.09	0.17	0.17	0.11
  ERA-40	0.64	0.11	0.02	0.11	0.22	0.17	0.11

  Process Based Benchmarks

  The following files contain benchmark data for the four dynamical benchmarks in the previous section, for NCEP/NCAR data only. The files contain the actual anomaly values for each of the 27 SSW events which allows you to construct your own box plots and other statistical plots. The benchmarks are in date order from the first SSW to the last and the dates correspond to the SSWs in the NCEP/NCAR reanalysis file here.

  
  &Delta T₁₀
  &Delta T₁₀₀
  &Delta U₁₀
  &Delta [v'T']₁₀₀
  

  Data Errors

  There are obviously lots of sources of error in a calculation of this type with a subjective benchmark. Firstly, there is not complete agreement between the reanalysis datasets on when SSWs occur or on the climatological structure of SSWs, ERA-40 is slightly more peaked in January then NCEP/NCAR for example.

  We have provided estimates of the standard error of the SSW frequency estimate so that statistical tests can be conducted and provided the raw data for the benchmark diagnostics so that inter-event variability can be estimated

  References

  The two papers which form the basis for this 'cookbook' can be downloaded (in preprint form) from LMP's website.
  
  • Charlton A.J., Polvani L.M., Perlwitz J., Sassi F., Manzinz E., Pawson S., Nielsen J.E., Shibata K. and Rind D. A new look at stratospheric sudden warmings. Part II. Evaluation of Numerical Model Simulations, in press , J. Clim. pdf
  • Charlton A.J. and Polvani L.M. A new look at stratospheric sudden warmings. Part I. Climatology and modeling benchmarks, in press , J. Clim. pdf
  Please feel free to contact either Lorenzo Polvani or Andrew Charlton for more details.

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  Last Updated: 2007-02-06
  Author: Andrew Charlton