## Betting on Climate Predictions

Pretend someone is willing to bet you $50 that El Niño will ** not** occur. Before you jump at it, you might want to know what the chances of El Niño are, right? So you then look up your favorite model prediction and discover there is a 90% chance of El Niño. The odds are in your favor. You go for it and take the bet.

But something happens and you lose. El Niño doesn’t occur. Oh the horror! Does that mean the model is totally useless? After all it forecasted a 90% percent chance of an El Niño and it didn’t happen. You might think that means the model was awful and next time you may not trust your money with such a prediction.

These sorts of bets occur all the time. And **probabilistic forecasts** (models that tell you there is a certain percentage (%) chance of an outcome) are becoming more popular. An example is FiveThirtyEight’s election and sports predictions.

But, despite their popularity, it is easy to misunderstand what these models are telling you. Normally, we like to think that a prediction is either “right” or “wrong.” However, there is value in such probabilistic models even when they appear to be flat-out “wrong.”

Let’s look more closely at your bet. There was a 90% chance of El Niño. That means there was a 10% chance of no El Niño. Phrased another way, it means that given similar starting conditions, 1 in 10 times El Niño won’t develop at all. Unluckily for you, the 1 non-El Niño time appeared on the very first try!

Maybe if you had hung in there and kept making bets, the next 9 times would all have been El Niños (1). You would have won $50 x 9 = $450! A nice chunk of change: that is why **it** **makes sense to play a long game. **But if you only played the game once, becoming discouraged in that first attempt, you would not have been able to take advantage of such a model because you might have thought the model was flat out “wrong.”

This can work the other way too. Say, in that very first turn, you won! There was a 9 in 10 chance of El Niño and then El Niño occurred. You assume this is a great model that is “right!” However, even that confidence is premature; in this one try, you just happened to be in that 9 in 10 moment. You very well could have been in the other category though it was less likely.

In fact, if the model is **reliable** 1 of the 10 times ** must** result in no El Niño (we don’t know when it will occur). It might seem strange, but a model is slightly

**unreliable**if it forecasts a 90% chance of a certain outcome occurring and that observed outcome actually happens 100% of the time (or any % other than 90%).

*In a reliable model, the forecast probability should equal the historical probability over a long observational record*

More simply: if you are flipping a coin, you would * forecast* that over a lot of coin flips, you would flip 50% heads and 50% tails. This is your prediction model: you expect the coin is equally weighted on each side and so there is a 1 in 2 chance of heads or tails. If the coin was heads in the very first coin flip, you don’t then assume your model is right or wrong. You assume that you haven’t flipped the coin enough to see whether your model is reliable. Over many flips (or long history), you should

*an outcome that is close to 50% heads and 50% tails.*

__observe__Sometimes we show how good a probabilistic model is in a **reliability diagram**. We look at a longer period of time (30 years of past forecasts, or hindcasts) and ask how good the model was in predicting the chance of El Niño. Now keep in mind, as Tony has described previously, there are three possible outcomes in ENSO outlooks: a % chance of El Niño, La Niña, and Neutral. Here is a reliability diagram for 6-month predictions from the CFSv2 model showing the reliability of probabilities of El Niño (red line that is labeled “above”) and for La Niña (blue line that is labeled “below”):

The straight, black diagonal line shows the result for an ideal model with *perfect reliability* (the forecasted chance = historical chance in observations). What this figure shows us is that CFSv2 provides “overconfident” predictions 6 months out (2). That is, when it forecasts a 90% chance of El Niño, El Niño is actually observed about 60% of the time (red line). The models generally become more reliable (closer to the black diagonal line) for predictions made closer to the time the forecast is made (e.g. lead-0).

Probabilistic forecasts might seem wishy-washy at first glance. Isn’t it just a way to cover one’s backside if a prediction is “wrong?” However, a single forecast is not enough to tell you whether your prediction is “good” or “bad.” It’s over the long haul, when making bets on probabilities can pay off.

###
**Footnotes**

(1) Odds are good that the next 9 times would not have all been El Niños because the system doesn’t remember whether or not the first time was an El Niño. It requires a longer period of time to make sure your bet fully paid off (and assumes a reliable model). The reason for this is that randomness dominates in shorter records. You can envision this randomness occurs when you flip a coin. It is not surprising to see a run of consecutive heads or tails: H – T – H – H – H – T. Over a longer period of time with more coin flips, the net outcome will occur closer to 50%, but in a shorter number of flips the coin and model might *seem* unreliable and will often will deviate from 50% in either direction.

(2) Note that this figure has some jagged curves… this is a reflection of the lower number of cases in some bins. If we had, say 100 years of past predictions, then we would have a better estimate how reliable the model is (see footnote #1). Also, this is showing just the “raw” data from CFSv2. At NOAA CPC, we statistically correct the raw model output from CFSv2 (using hindcasts of CFSv2 data) in order to obtain predictions with better reliability. Despite the correction, CFSv2 remains slightly overconfident for long lead forecasts. Here is an example of what a statistically adjusted CFSv2 reliability diagram looks like (same as the figure above except adjusted using the statistical correction in Barnston and Tippett, 2013):

###
**References**

Barnston, A.G, and M. K. Tippett, 2013: Predictions of Nino3.4 SST in CFSv1 and CFSv2: a diagnostic comparison. *Clim. Dynam*., 41, 1615-1633. (open access)

## Comments

## Thanks for the great article!

Thanks for the great article!

## RE: Thanks for the great article!

They also have a good illustrator! ;)

## Is La Nina more predictable than El Nino?

First of all, I really enjoy all the blog posts (and the cartoon in this one). From the reliability diagrams, it looks like the CFSv2 is much better at getting the probabilities right on La Nina than on El Nino. Is that the correct interpretation and does it mean that La Nina is more predictable than El Nino? Or is just a sample size issue with more La Nina cases to make the statistics settle down?

Has anyone tried looking at a reliability diagram in three dimensions with lead time on the z-axis. It would make for an interesting "reliability surface".

## RE: Is La Nina more predictable than El Nino?

There are many measures of prediction skill and "reliability" is only one of them. At this point there is no evidence that we're aware of that says that La Nina is more predictable than El Nino. However, in this *one model* the reliability score does seem to suggest probabilities assigned during La Nina are better than that of El Nino. Sample size could play a role as well. And in any case, this result doesn't necessarily translate to other models.

You're other idea is interesting and not one that we've ever looked at. Agreed it would make an interesting figure, possibly something we'll look at in the future.

## This was a very informative

This was a very informative article. A suggestion on future articles would be to help explain some of the graphs seen in the ENSO weekly update. I am not sure what to look for in the charts of Outgoing Longwave Radiation, Wind Speed and Upper-level Velocity Potential Anomalies.. They seem like they should be showing the atmospheric response of El Nino and La Nina events.

## RE: This was a very informative

Thanks for the suggestion. It's something we'll certainly consider doing. At this point, the atmospheric fields are not reflective of El Nino, and is a significant reason why we have yet to declare that El Nino has arrived.

## reliability

Hi. An old statistics joke goes something like this: “One out of every 20 people is crazy. So, think of your 19 closest friends. Are any of them crazy? If not, then it must be you!”

This joke exemplifies the same type of error made in the sentence “In fact, if the model is reliable 1 of the 10 times must result in no El Niño (we don’t know when it will occur).” The model could be reliable even if, in all 10 of the first 10 times, El Nino did occur. Or even if it didn’t occur even once. Statisticians frame the difference between theory & observation as one of “populations” vs “samples” or “hypotheses” vs “data.”

True, any observed proportion of El Ninos occurring other than 90% does support best an alternative hypothesis, rather than the hypothesis that the theoretical “population” proportion is 90%. It does not imply, though, that the model is unreliable. The most we can do is collect large numbers of observations, calculate the observed proportion of El Ninos, & then measure the strength of evidence for or against the model’s reliability.

## RE: reliability

Well, I'm not the crazy one :-) I agree that we could have played up your point a bit more in the article, but we decided to keep the math simple as possible. Footnotes (1) and (2) describe the point you're making here which is that 10 is way too small of a sample to obtain proper reliability statistics. Ideally, we'd have thousands of samples. Even the reliability figures that we show you which are based on 30 years of model hindcasts are not long enough and have some degree of error associated with the estimate. Thanks for weighing in and reinforcing this point-- complete with a great joke!

## AGEN JUDI BOLA TERPERCAYA

Thanks for the suggestion. It's something we'll certainly consider doing. At this point, the atmospheric fields are not reflective of El Nino, and is a significant reason why we have yet to declare that El Nino has arrived.

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