Probability, Climatology, and Forecasting


Chuck Doswell

Posted: 14 August 2003 Updated: 25 March 2007 - some minor revisions and corrections.

This essay is, as usual, just an expression of my opinions ... and hopefully might be helpful. Comments and eedback are always of interest ... e-mail me at This essay is not peer-reviewed science, nor does it reflect the views of any organization that now employs me or ever has in the past. In point of fact, organizations typically have no viewpoint at all! Only people have viewpoints ... but I digress ...

1. Introduction

This content grows out of some discussions I've had with my colleagues and students. The question has arisen about the role of climatology in probabilistic forecasting. How does one use climatology in forecasting the weather?

I believe the place to begin this discussion is to consider some elementary concepts that connect the science of meteorology to the subdiscipline of climatology. With that established, then some points about probabilistic forecasting are made that are connected to the topic. Finally, these separate parts can be connected in such a way that the answer to such questions is obvious.

It's my perception that many folks new to the concepts of probabilistic forecasting are likely to be confused by the questions raised. Hopefully, this will clarify the topic.


2. Meteorology and climatology

I want to reemphasize some points made elsewhere, in a different context: the notion of what is "normal" regarding the weather is essentially a matter of averaging the weather in some way. Like the concept of "normal", the climate is in a very real sense simply an expression of some sort of average of the weather. Climate changes in response to persistent, systematic changes in the weather. If we had the data, we could (at least in principle) determine the average climate since the Earth began. Obviously, we don't have the data to come even close to this. Hence, we tend to compare whatever knowledge we have about climates of the past to what is now occurring. The standard is now, apparently. However, the averaging period can vary, and so it's not some sort of semantic error to speak of the climate changing. The climate clearly has been very different in the geologic past and is probably going to continue to change so long as the planet has an atmosphere.

For most laypersons, the climate is what they themselves have experienced. Clearly, the atmosphere will not have demonstrated the full range of its possibilities to any one person even over the course of an entire lifetime. It's obvious that some events occur pretty infrequently, and so when rare events occur, they're often characterized as "freak" events. Many people have a lot of trouble imagining anything beyond their life experience. Such events might well be common when viewed from a geologic time scale.

Anyway, this is distinct from events like tornadoes which, although they are extremely rare at any one point, actually occur relatively frequently. I've already discussed the statistics of violent tornadoes here ... they are rare events only in the limited perspective of sitting on one particular spot. If we consider the entire 48 contiguous states, it is borders on absolute certainty that at least one violent tornado will occur somewhere within that area during the course of any given year.

The actual number of violent tornadoes in the 48 contiguous United States in any given year fluctuates, of course. Tracking those fluctuations and considering what the average number in a year is a matter for climatology. A study of the occurrence frequency of violent tornadoes over some period encompassing several decades would be described as a "climatological" work. But the number of violent tornado events in a year is strongly dependent on the meteorology that has gone on through the course of that year. In years with certain persistent large-scale weather patterns, violent tornadoes will occur much more frequently than years with some other persistent large-scale weather pattern. In some years, the large-scale weather pattern fails to be persistent at all, and that fact would likely have a different impact on the number of violent tornado occurrences that year. The details matter ...

The large-scale weather pattern undergoes changes in part because of meteorological processes that may or may not be well-understood, but the weather is also connected to the oceans (which have their own internal dynamics of complexity quite comparable to the atmosphere itself) and the specific distribution of land and sea, as well as the changes in terrestrial elevation. Over long periods, the details of the Earth's orbit around the sun can cause climate change - in fact, such changes are likely responsible to some extent for alternations between ice ages and warm periods. Further, there are extraterrestrial influences on the weather, notably fluctuations in solar output, as well as tidal influences from the sun and moon. Finally, the very composition of the atmosphere alters the weather, as we have recently found through studies suggesting anthropogenic influences on the atmospheric "greenhouse" effect. It's safe to say that we're now only beginning to appreciate the complex, nonlinear processes that control the weather. Anyone claiming to understand those complexities in detail is a liar, or a fool, or both.

The point of all this is that the climate is hugely difficult to grasp and given that we have only begun to do something reasonably scientific and comprehensive with the atmospheric part of the problem in the last 55 years suggest we have a long way to go to understand the climate.

Having said all this as a means of suggesting that climatology is still a very young discipline within the general field of meteorology, let's return to the relationship between the climate and the weather. Climate is concerned with the long-term behavior we observe and try to understand. Weather is the short-term behavior that when averaged and tabulated becomes the grist for the climatologist.

It is clear that the range of what is likely to be observed on any given day is constrained by the climatology. Let me clarify what I mean by the last statement. For example, in central Oklahoma, it is very unlikely to be below 0 deg C during the first week in August. The reason it is usually hot and virtually never has been observed to be below 0 deg C in central Oklahoma during the first week in August is climatological. However, the fact that a temperature below 0 deg C has never been observed in Oklahoma during the first week in August does not preclude that such an observation is possible (i.e., its probability is not zero). In fact, there's some evidence to believe that at some time in the distant past, when the climate was very different than now, such temperatures might have been commonplace, whereas temperatues of 40 deg C (104 deg F) or higher would have been extremely rare.

Allow me to make this somewhat more specific with another example that's closer in spirit to where I'm headed with this. On any given day in Oklahoma, for a specific square mile somewhere in the central part of the state, it's quite unlikely that a violent tornado will occur. The frequency in the early part of May within an area of about 2000 square miles is about 50 events in 1000 years ... see here for some pertinent information about such probabilities ... so for any particular square mile, it's on the order of a few events in 10,000 years. That's for the maximum observed frequency of violent torndoes in early May. Thus, the average frequency on any randomly chosen day of the year for that particular square mile in central Oklahoma might be around one event in 10,000 years. That's a pretty rare event, right?

But on the evening of 3 May 1999, the chances for a tornado in central Oklahoma were much higher than that. On this particular evening, the atmosphere was not configured in any ordinary way. Instead, it was so configured that an outbreak of tornadoes was underway. Virtually by definition, tornado outbreaks of the magnitude of what happened on 3 May 1999 are quite uncommon. Not all tornado outbreaks arise in the climatologically favored time and place that was early May in central Oklahoma, as did the 3 May 99 event. Major outbreaks of torndoes have occurred in Massachusetts (during the 9 June 1953 situation that produced the Worcester, Massachusetts tornado), or in the dead of winter on the Central plains (the MO-IA-IL situation on 24 January 1968), to name just two examples of "freak" events. On such days, the atmosphere is much more likely to produce a violent tornado than on any randomly-selected day in the climatological record.

Therefore, the relationship between meteorology and climate is that the atmosphere doesn't know anything about the calendar, the map, or the clock. What I mean by that is that weather events can and do occur on dates, at locations, and at times when they are climatologically infrequent. Hence, it should be clear that the processes responsible for particular weather events are not influenced directly by climatology. What is common or "typical" on that date, that location, and that time of day is influenced heavily by climatology, however!


3. Probabilistic forecasting and climatology

Probabilistic forecasting is intended to express uncertainty. Only on relatively rare occasions is the forecast so obvious that a forecaster can be 100 percent confident in the accuracy of the forecast. Harold Brooks and I have discussed this process here and here, so I'm not going to go into most of those details here.

What matters is to understand that the probability of some event during some time period and within some finite region is a conditional probability. For example, the probability of a tornado during the time from 5 p.m. to 7 p.m in central Oklahoma on 3 May 1999 is much higher than the climatological average for such a period in that location. If you were to express that climatological probability, it would be so low that for all practical purposes, the event is nearly certain not to happen. But the weather pattern for that particular space-time volume suggested pretty strongly that the probability of a tornado was not vanishingly small. Rather, those conditions made it pretty obvious that a tornado was about to hit the Oklahoma City metropolitan area (the "OKC metro?). Note that even with a tornado already observed and doing damage in the countryside, heading toward OKC, the conditional probability would not be 100 percent! That particular tornado could dissipate, or it could swerve suddenly and miss the OKC metro, or whatever. Thus, absolute certainty is something rare.

If it's true that the weather doesn't recognize the calendar, the map, or the clock ... nevertheless, this event occurred very near the climatological peak for such events in both space and time. Hence, this event was, in a sense, a "normal" violent tornado! When violent tornadoes occur in early May during the evening in central Oklahoma, they're as consistent with climatology as it's possible to be ... even though such events are statistically rare. The climatology shows that the atmosphere concatenates the conditions necessary for violent tornadoes (whatever those might be!) most frequently in this location, at this time of year, and at this time of day. When violent tornadoes occur in regions where the climatological frequency of such events is much lower ... say, Minnesota in the winter during the morning, then such events would be considered "freak" events by many. The climatological frequency of such events is low, but it is not zero.

If you are forecasting for tornadoes, it likely would seem odd to put out a tornado warning for a storm in Minnesota in the winter during the morning and it might be difficult to "pull the trigger" for such a strange situation. My experience in forecasting is that many forecasters indeed are reluctant to acknowledge that the conditional probability of some event is determined by the weather, not the climatology!

So does climatology have any role to play in forecasting? Absolutely. In the first place, if a forecaster knows absolutely nothing that would distinguish the weather on the day in question from any randomly-selected day in the climatological record, then the forecast probability should be climatological frequency. Many people believe that a "know-nothing" forecast is a "coin flip" - that is, a 50% probability. As already explained, that would be an enormously high probability if the forecast event was for a tornado in Minnesota on a winter's morning! Hopefully, a forecaster often can do better than to "go with climatology". But knowing the climatology is a good place to start making a probability assessment.

For example, if it seems that the meteorology is suggesting one thing and the climatology is suggesting something else, this can add to a forecaster's uncertainty. If probabilistic forecasting were an option, forecasters could express their uncertainty without having to make that agonizingly difficult yes-no, binary decision. Climatology is what is for a reason ... presumably, it's unusual for all the ingredients for some event to be brought together in a particular space-time volume. Since our understanding of the atmospheric processes associated with that event is never perfect, we can use the climatology to alter our perception of the likelihood of an event. In the case of tornadoes and other climatologically "rare" events, the difference between the climatological frequency and the conditional probability associated with the ongoing weather can be quite large ... several orders of magnitude, in fact! Thus, it is dangerous to "hedge" the forecast very far in the direction of climatology, because going very far toward that climatology would reduce the estimated probability below anyone's threshold of utility. If you're going to mention an event in the forecast, its conditional probability of occurring (i.e., given the current weather situation) must exceed some threshold value. Where to put that threshold should be based on knowledge of the climatological frequency.

Note that scale of the forecast space-time volume has a lot to do with this. Recall that if we consider a space-time volume that includes the entire area of the 48 contiguous states for an entire year at any time of day, the probability of one or more violent tornadoes in that space-time volume is near 100 percent ... at least for the existing state of the climate. The climatological frequency of tornadoes in Oklahoma in May during any randomly-selected 24 hour period is considerably lower than 100 percent. For the folks in the Storm Prediction Center, the threshold probability for even mentioning tornadoes in their probabilistic forecasts is 2 percent (for an event defined as 1 or more tornadoes within a 25 mile radius of a point during the forecast period), which means that even that seemingly small value is notably higher than the climatology! For tornado touchdown point climatology, see the NSSL Hazards Page.


4. So what does this mean for forecasts?

The preceding suggests where I think climatology plays a role in forecasting. It's important and useful to know what the climatological value for some forecast event actually is. As I've tried to explain in the essays by Harold Brooks and me (see above), climatology is essentially a "know-nothing" forecast. If you don't have a clue what's going on meteorologically, a safe forecast is either persistence (forecast a continuation of what has recently been going on, whatever it is) or climatology. If you have objective forecast probabilities and are unable to justify changing them on the basis of your understanding of the situation, then your best forecast is the guidance product.

In order to have a proper knowledge of climatology, however, it's vital to specify the space-time volume used for the averaging. The climatology and the forecast period should be matched to the same space-time volume. For tornadoes, it makes a huge difference, as I've been suggesting.

Further, the definition of an event plays a big role in determining the climatology and, not coincidentally, in determining the conditional probability based on the weather situation. Clearly, again, the forecast and the climatology should be using the same definition for an event. If we forecast tornadoes, but the climatology is for radar-detected vortex signatures, those are not precisely matched. They might well be strongly correlated, but that's quite distinct from a match.

Some events are much more likely than others, so the "know nothing" threshold probability varies with the climatology of the event - and depends on how much knowledge you have of how the event frequency varies. During the warm season over much of the Plains, the climatological probability of measureable rain in the area of a WFO forecast area of responsibility during a day is around 20-30 percent. If you forecast 20-30 percent, you're essentially saying that you can't distinguish the probability of measureable rain on that particular day (say, 23 May 2003) from any randomly chosen 23 May in history. This is the reality of that forecast, whether or not the forecaster intends to make such a statement. Again, a forecast of 50 percent probability of rain in this case is not "just a coin flip" ... it actually says the chances are higher than climatology, a relatively strong statement about the likelihood of rain.

Thus, knowing climatology is helpful in deciding how to estimate one's uncertainty. It is a sort of gauge by which a forecaster can attempt to calibrate forecast uncertainty. Beyond this use, climatology is something that frequently must be overcome in attempting to diagnose the conditional probability of some weather event in the forecast, based on the actual, ongoing weather at the time. That is, a forecaster should strive to forecast the weather, not climatology! In situations where the forecaster is at a loss to be able to arrive at a conclusion about what is likely to happen, climatology is a safe forecast. But it does little good to forecast climatology every day, day after day. This winds up being a no-skill forecast! It might be accurate on average, but it would exhibit none of what we mean in forecast verification terminology by the word "skill." Surely forecasters can do better than that!