# Potential predictability

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

${\displaystyle \sigma ^{2}=\sigma _{\nu }^{2}+\sigma _{\varepsilon }^{2}}$

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

${\displaystyle p={\frac {\sigma _{\nu }^{2}}{\sigma ^{2}}}={\frac {\sigma _{\nu }^{2}}{\sigma _{\nu }^{2}+\sigma _{\varepsilon }^{2}}}}$

The signal to noise ratio is defined as:

${\displaystyle \gamma ={\frac {\sigma _{\nu }^{2}}{\sigma _{\varepsilon }^{2}}}}$

${\displaystyle p}$ and ${\displaystyle \gamma }$ can be computed from each other:

${\displaystyle p={\frac {\gamma }{1+\gamma }}\qquad ,\qquad \gamma ={\frac {p}{1-p}}}$

We have ${\displaystyle 0. Small values of ${\displaystyle p}$ indicate that the signal is small, and that the weather is inherently unpredictable. Values of ${\displaystyle p}$ 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]

## References

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