YODEN Shigeo

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for SPARC Temperature Trend Meeting at Tabard Inn
in Washington DC April 12-13, 2007
Seasonally Dependent Detectability of a Linear
Trend Submitted to JGR

• YODEN Shigeo
• Dept. of Geophysics, Kyoto Univ., JAPAN
• Highlights

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• detectability of a linear trend in a
  finite-length dataset
• natural internal variability causes a spurious
  trend
• it may have a non-Gaussian nature
• we argue
• the minimum length of dataset necessary for the
  detection of a given magnitude of trend with a
  given statistical significance level
• the minimum magnitude of trend for a given length
  of dataset with a given statistical significance
  level
• Edgeworth expansion
• of the distribution function of the spurious
  trend
• estimation of higher moments by long time
  integrations of numerical models under a purely
  periodic annual forcing
• two examples
• stratospheric polar temperature (15,200-year
  dataset)
• precipitation (1,000-year dataset)

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• Labitzke diagram
• seasonal variation of histograms of monthly mean
  T (30hPa)

model output could be used to estimate the moments
observational data are too short
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• the minimum magnitude of trend for a 20-year
  dataset with the confidence coefficient of 90

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• statistical significance of the three trends
  estimated with the moments of our numerical model
  output

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• Concluding remarks
• The detectability depends on distribution
  function of the spurious trend due to the limited
  length of dataset with natural internal
  variability.
• Gaussian Students t distribution of the
  spurious trend
• Non-Gaussian use of the Edgeworth expansion
• We can estimate the distribution function with
  the moments of the internal variability obtained
  by long time integrations of atmospheric
  numerical models.
• ? the minimum length of dataset necessary for the
  detection of a given magnitude of trend
• ? the minimum magnitude of trend for a given
  length of dataset

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• Two typical examples that have large seasonal and
  regional dependence of natural internal
  variability
• stratospheric polar temperature in the Northern
  Hemisphere
• precipitation in the equatorial region
• The detectability has large dependence on season
  and region.
• it is not always appropriate to use annual or
  global average
• careful consideration is necessary to choose
  season and region as well as quantity for
  detection of a statistically significant linear
  trend with a given length of dataset