S2S Empirical Prediction Model

An empirical prediction model developed at Colorado State University for S2S prediction of surface variables based on the MJO.
Additional details can be found on the README tab.

Click a location in the lower 48 states or Alaska. Analysis is done over a 7.5 x 7.5 degree box centered on that point.

Choose the climate indices on which to base the model.
Set the model parameters.
Statistical significance.
Choose the colorbar range (units of HSS). Values out of range are assigned the darkest color.

Forecasts of opportunity are defined as phase/lead combinations with statistically significant Heidke Skill Scores (alpha = 0.05). All results here are for a 5-day averaging window of the predictand.
Choose the climate indices on which to base the model.
Set the model parameters.

Overview of the web app

This web app allows users to view thousands of combinations of empirical model predictions of sensible weather anomalies using the Madden-Julian oscillation (MJO), the quasi-biennial oscillation (QBO), and the El Nino Southern Oscillation (ENSO) as predictors out to 6 weeks. The app allows you to visualize model composites, predictions, and skill.

Model details

The MJO is based on the RMM index for all analysis, except for temperature which uses ROMI. Phases of the climate indices are defined using a 0.5 sigma cutoff.

Averaging window of variable: The anomalies of the forecast variables are averaged over a 5-day window beginning on the given forecast lead (or lag) day. For example, a day 6 forecast implies a forecast valid for a 5-day period 6-10 days after initialization. Other averaging windows are available.

Significance of composite plots: Statistical significance of the composites is calculated using a block bootstrapping method described in Mundhenk et al. (2018) and Baggett et al. (2018). Currently, the number of iterations used is 50.

Significance of HSS plots: The statistical significance of the HSS is assessed using the random walks method from DelSole and Tippett (2016). Phase and lead combinations with HSS that are significantly better than a random forecast at the 95% confidence level are considered skillful forecasts of opportunity.

Skill quantification: Forecasts are verified using a leave-one-year-out cross-validation procedure (see Johnson et al. 2014 and Mundhenk et al. 2018) that tallies correct and incorrect forecasts. Model skill is measured using the Heidke Skill Score (HSS): HSS = 100 x (C-E) / (T - E). C is the number of correct forecasts, and E is the expected number of correct forecasts by random chance. Since the model predicts anomalies based on the climatological median, a random model is expected to be correct at a rate of 50%. Based on this formula, an HSS of 30 implies that the model is correct 65 out of 100 times (or correct twice as often as incorrect).

Additional References

* Nardi, K.M., E.A. Barnes, E.D. Maloney, C.F. Baggett, D.S. Harnos and L.M Ciasto: Skillful all-season S2S prediction of U.S. precipitation using the MJO and QBO, in prep.

* Mundhenk, Bryan, Elizabeth A. Barnes, Eric Maloney and Cory F. Baggett, 2018: Skillful Empirical Subseasonal Prediction of Landfalling Atmospheric River Activity using the Madden-Julian Oscillation and the Quasi-biennial Oscillation. npj Climate and Atmospheric Science, doi: 10.1038/s41612-017-0008-2

* Johnson, N. C., D. C. Collins, S. B. Feldstein, M. L. L'Heureux, and E. E. Riddle, 2014: Skillful Wintertime North American Temperature Forecasts out to 4 Weeks Based on the State of ENSO and the MJO. Weather Forecast., 29, 23–38

* DelSole, T., and M. K. Tippett, 2016: Forecast Comparison Based on Random Walks. Mon. Weather Rev., 144, 615–626.


The initial empirical model based on the MJO and ENSO was developed by Johnson et al. (2014) for temperature. Mundhenk et al. (2018) extended the model to include the QBO for atmospheric rivers. All of the calculations for all variables used here were coded and organized by Kyle Nardi (see Nardi et al., 2019), supervised by Eric Maloney, Elizabeth Barnes, Dan Harnos and Laura Ciasto. The shiny web app was written by Elizabeth Barnes with server support by Matt Bishop.


Funding for the development of this emprirical prediction tool and web app comes from NOAA Climate Test Bed grant NA18OAR4310296 and NOAA MAPP grant NA16OAR4310064.