Seasonal Heteroscedasticity: Why 10 Degrees Above Normal Is A Bigger Deal Now Than Ever

Seasonal Heteroscedasticity: Why 10 Degrees Above Normal Is A Bigger Deal Now Than Ever

Some weather geeks were paying close attention to southern California early last week. An unusually hot Santa Ana wind event was underway from late Sunday the 23rd, through Tuesday the 25th. Long Beach hit 105 degrees both Monday and Tuesday, and much of the LA Basin was between 100 and 105! That’s simply unheard of this late in the season, even in SoCal. Normal late October high temps are in the 70s along the immediate coast, and about 80 if you’re somewhat inland – so most spots were somewhere between 20 and 30 degrees above seasonal norms!

To put it in perspective, that would be the equivalent of The Dalles or Portland having a couple sunny 80-85 degree days at this time of year. HOWEVER…and I’m not afraid to say this…I’m quite confident we will never see anything of the sort in the last week of October here. (At least not in the next five to seven decades; heat up the planet enough and anything becomes possible.)

Those of us who’ve lived in the Pacific Northwest long enough, know that pre-Halloween weather in our climate is slightly tepid at best – and very chilly, wet and dark at its worst. The Dalles DID manage to make 73 last Wednesday and Portland pulled off an impressive 3 days in the low 70s Thursday-Saturday, thanks to some warm east wind much like the Santa Anas. But the fact remains that late October & early November is actually the least variable time of year, in terms of departures from normal high temps.

But why? Why is a departure of X degrees above (or below) seasonal norms, more “impressive” now than it would be in spring or summer?


The phenomenon I am referring to is called SEASONAL HETEROSCEDASTICITY. The term heteroscedasticity literally means “different spreads.” It comes up most often in the world of statistics and econometrics, where it is known mainly as a nuisance when trying to create models. But in the context of climatology? Basically it means that, due to the idiosyncracies of our climate region and the seasonal cycle, temperatures fluctuate more widely or more narrowly at different times of the year.

Don’t Forget Deviation!

Climatologists and weather nerds are very used to thinking of data in terms of averages. For example, if we say that the average high in late October is 60 degrees, it means that there is roughly a 50-50 chance that our max temp will be either above or below 60 on any given late October day. (It isn’t always a perfect 50-50 split; don’t confuse average with median!)

But there is another vital component to a data distribution, namely, the standard deviation. This tells you how prone the temperature on a given date, is to fluctuating from one year to the next. The general rule is that, if we ignore whatever the weather forecast is trying to tell us, then there is a two-thirds chance that the high (or low) temperature on any given day will fall within one standard deviation of the “normal” high or low.

In other words, suppose the normal daily maximum temperature on April 30 in some location, is 75 degrees F and the S.D. is 8 degrees. That means that in roughly two out of three years, the high temp on April 30 will be somewhere between 67 and 83. One-sixth of the April 30ths will be hotter than 83, and about one-sixth will be colder than 67. High temps more than two SDs away from the norm – in this case, hotter than 91 or colder than 59 – are generally considered unseasonable since the chance of either one occurring is less than 5%.

Most daily record high and low temps are between 2 and 3 SDs outside the norm, though in extreme cases (such as some arctic blast nights), the departure can be 4 SDs or more.


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Heteroscedasticity: Lows vs Highs

The actual value of our daily standard temperature deviation, however, fluctuates with the seasons. Our low temp SD is smaller in the summer months, about 5.3 to 5.6 degrees. Nighttime temps are most variant around January 1, when the low temp SD is near 8.0 F.

This one is fairly straightforward to explain: first, all things equal, cloudy nights are warmer than clear nights. But secondly, not all is equal: in the summertime, clear airmasses are normally warmer than cloudy airmasses (think a super-hot “Death Ridge” as opposed to a cool North Pacific trough in June or July). So the “airmass effect” and the “cloud insulation effect” are partly cancelling each other out, much of the time during the summer.

The result is that our temperature departures during heatwaves are usually quite a bit larger for the highs, than for the lows. And when a cool cloudy pattern is trolling your July or August BBQ, it never gets the chance to really plummet at night. But in winter, clear airmasses are often as cold or colder than cloudy ones. Adding snow cover to the equation only exacerbates the effect. Winter nighttime temps vary from downright balmy during a Pineapple Express, to single digits during a severe outbreak of arctic air.

Far more curious is what happens to the variance in high temps over the seasons. There are actually two “tight points” in the year when the SD is relatively small: it drops to about 6.5 in mid-March. But the narrowest regime of all occurs in late October and early November. Here the SD is as small as 6.2 to 6.3 degrees F. Meanwhile it peaks at 9.0 in late December and 9.2 in late May. What is going on here?

Development of inversion season is probably the best explanation as to why we don’t get intense warm spells in the PNW lowlands in late October / early November. The warm 850mb levels of an upper-level ridge in late fall, get undermined to a degree near the surface due to long nights and weak sun. This effect combines with our rapidly falling average high temps, to create a spectacular plunge in our “warmth potential”: the same kind of massive West Coast ridge that could have The Dalles flirting with 90 degrees on October 1, might not even get us to 70 if it happens at Halloween.

At the same time, the really cold arctic and sub-arctic airmasses haven’t fully developed by this time, at least in most years. And the sun angle is still strong enough to somewhat “nerf” the cold departures during daytime, if a dry ‘preseason’ arctic airmass does develop a la 2002 or 2003.

In the case of March, the big culprit behind the tight high-temp SD is that the airmasses just don’t get wildly warm or wildly cold, except in rare circumstances. In fact, west of the Cascades, the month of March has the coolest 850mb normal temps of all!

Hitting 70 or 72 at DLS for the first time in mid-March may feel lovely after all the winter chill, but in truth, that’s only about 13-15 degrees above the normal high temp…or 10-12 degrees if it happens toward the end of the month. And by March 15, it’s pretty tough to stay below 45 degrees all day long, either. Cold airmasses in March tend to suffer from “reverse inversion effects” at the surface: strong sun angle means that during sunbreaks, the chill is undermined at the very lowest levels. That’s how we can have a dusting of snow on a March morning, followed by temps well into the 40s during the afternoon.

As springtime progresses, the North Pacific troughs stay pretty chilly while the upper-level ridges become much warmer under the powerful sun. This leads to our high-temp SD peaking in late May and early June. Think of it: we’ve been in the 100s before on rare occasions at that time of year. But a late-season trough can still quite easily keep even The Dalles below 70 degrees for a few days in early June.

The Dalles vs. Portland vs. Other Climates

The annual SD profile for Portland low temps looks just like a narrower version of The Dalles – bottoming out at about 3.3 in early August and peaking at 6.7 near the New Year. And the only difference in the high-temp SDs (besides being a bit narrower overall), is that there is not as much of an uptick in early winter, and no 2nd tight period in early spring. I don’t have a good theory as to this particular difference, though it might have something to do with inversions & arctic blasts having a slightly smaller “impact” on overall winter temperature regimes at PDX, as opposed to DLS. These are the two patterns where the chilly “continentiality effects” of weak sun, are most pronounced in the Columbia Basin.

And just for fun, I even looked at high-temp SDs for the USC campus in downtown Los Angeles. (I chose USC, because LAX is a bit too close to the cool Pacific Ocean to be a good representative of the LA Basin as a whole.) It’s completely different: persistent summer marine air tends to hold down departures between May and August, while the hot santa-anas allow for a “fall peak” in the 2nd week of October instead! Then the high-temp SD yo-yo’s up and down throughout the entire cooler half of the year, with two “spring peaks” in February and April. Throughout the late-fall and winter months, however, high temps are more variable than they are in summer, not less like in the PNW.

Obviously, climates at the latitude of Southern California don’t have the same kind of winter inversions that we do, due to the sun remaining stronger further south. And the brisk ocean surface plays a major role in keeping the immediate CA coastline cool in the summertime…while the interior sizzles almost every day. But even places like Roseburg and Medford manage to have better warm spells in early spring & late fall, than Portland and The Dalles do.

So there is my take on our HETEROSCEDASTIC seasonal temperature regime…and why our late fall warm spells for the PNW lowlands don’t get much better than what Portland saw late last week. You have to go a little bit further south to get the epic “Summer in Fall” kind of days, and somewhat north before winter can still make a solid impact on the month of March.

Here are some of the links to the SD data for the various stations. Click on ‘Daily Tabular Data’ under the 1981-2010 caption for the most current average & SD charts:

The Dalles (DLS)

Portland (PDX)

Medford (MFR)

Los Angeles @USC:



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