Potential predictability explained

The term potential predictability is used in the context of weather forecasting to describe the extent that the future weather can be predicted in principle, i.e., it describes the proportion of variance in the weather that arises from systematic factors rather than random noise.^{[1] [2] [3]}

Mathematical formalization

Denote by

\sigma the standard deviation in weather outcomes, so that \sigma ^{2} is the variance in weather outcomes. Of this, denote by \sigma ^{2} _{\nu} the internally generated variance component and by \sigma ^{2} _{\varepsilon} the unpredictable noise component. We have:^[1] \sigma ^{2} = \sigma ^{2} _{\nu} + \sigma ^{2} _{\varepsilon}

The potential predictability variance fraction (ppvf) is defined as:

p = (\sigma ^{2} _{\nu})/(\sigma ^{2}) = (\sigma ^{2} _{\nu})/(\sigma ^{2} _{\nu} + \sigma ^{2} _{\varepsilon})

The signal-to-noise ratio is defined as:

\gamma = (\sigma ^{2} _{\nu})/(\sigma ^{2} _{\varepsilon}) p and \gamma can be computed from each other:p = (\gamma)/(1+ \gamma) , \gamma = (p)/(1- p)

We have

0 < p < 1 . Small values of p indicate that the signal is small, and that the weather is inherently unpredictable. Values of p close to 1 suggest that the weather is potentially predictable, even if current weather prediction methods do not predict it successfully.

Research

Potential predictabilities have been estimated for different aspects of the weather and climate system, including heat transport,^[3] the Madden–Julian oscillation,^[4] and precipitation.^{[5] [6]}

Notes and References

1. Web site: Forced and internally generated 21st century decadal "potential predictability". Boer. G. J.. April 19, 2014.
2. Decadal potential predictability of twenty-first century climate. 10.1007/s00382-010-0747-9. Boer. G. J.. Climate Dynamics. 36. 5–6. 1119–1133. March 2011. 2011ClDy...36.1119B . 129591785 .
3. Potential Predictability of the North Atlantic Heat Transport Based on an Oceanic State Estimate. Journal of Climate. 25. 24. December 2012. American Meteorological Society. Tiedge. Bente. Köhl. Armin. Baehr. Johanna. 10.1175/JCLI-D-11-00606.1. 8475–8486. 2012JCli...25.8475T . free.
4. Web site: Potential Predictability of the Madden–Julian Oscillation. Waliser. Duane. Stern. William. Lau. K. M.. Jones. Charles.
5. Web site: Potential Predictability of Precipitation: Occurrence or Intensity?. Gianotti. Dan. Anderson. Bruce. Salvucci. Guido. April 19, 2014.
6. Potential predictability of the Asian summer monsoon on monthly and seasonal time scales. Mohan. R. S. Ajaya. Goswami. B. N.. 10.1007/s00703-002-0576-4. Meteorology and Atmospheric Physics. June 12, 2003. 84. 1–2. 83–100. 2003MAP....84...83A. 55128611.