Monday, December 15, 2014

Seasonality of PDO Influence

Mean daily temperatures in Fairbanks have been almost constantly above normal since the beginning of November, and the PDO phase has become strongly positive (see charts below).  Given the recent PDO behavior, the persistence of unusual warmth is no surprise, as we discussed in a post on November 27.

I thought it would be interesting to look in a bit more detail at the seasonal variations in the PDO influence on Fairbanks temperatures - for example, does the PDO influence peak in December, or is it equally large at other times of the year?

To address this question, I first looked at monthly data and examined the outcome in months for which the PDO index was in the top or bottom quartile of the 1930-2013 historical distribution.  This gives a sample size of 21 on both ends of the PDO distribution.  The first chart below shows the percentage of months in which the Fairbanks temperature anomaly had the same sign as the PDO index, and the second chart shows the median monthly temperature anomalies as well as the 25th and 75th percentiles of the temperature anomalies.  Note that I used the "normal" for the entire history (1930-2013) and did not adjust for long-term trends.

Looking first at the positive PDO, the first chart shows that December is indeed the month in which the positive PDO phase most reliably causes above-normal temperatures in Fairbanks (18 of 21 years), but the second chart indicates that the median anomaly is not as high in December as in November or January through March.  Also, the second chart reveals that there are large and interesting differences in the width of the conditional temperature distribution during the positive PDO phase.  For example, in November the positive PDO temperature distribution is quite narrow, with over 80% of years having a mean anomaly above +3 °F, but in January the temperature distribution is wide during positive PDO years.  We infer that the positive PDO is a much more useful predictor for Fairbanks temperature in November than in January; but the PDO signal becomes quite robust again in February.

The temperature behavior during the negative PDO phase is largely a mirror image of the positive PDO behavior, except during June-August when the negative PDO has almost no influence on Fairbanks temperature.  November is clearly the month in which the negative PDO most reliably causes below-normal temperatures in Fairbanks.  The negative PDO signal is much weaker in January, then picks up again in February, although with a large amount of temperature variance.  Overall, winter temperatures are more variable when the PDO is negative, leading to the conclusion that a negative PDO phase is somewhat less useful as a seasonal forecast predictor than a positive PDO phase.

Another way of looking at the data is to examine the distribution of daily temperature anomalies during positive and negative PDO phases (see charts below).  Here I used the prior 30-year climatology of daily mean temperature to obtain the daily anomalies, and I ran the calculation over sliding 21-day windows throughout the year, with the PDO index interpolated from the monthly values to the center of each date window.  The purpose of doing this is to see if there are any notable sub-monthly features of the climate during positive or negative PDO phases.

The charts above show quite a number of interesting features, but I'll only mention a few.  First, the response of daily Fairbanks temperature to the positive PDO phase seems to be relatively stable in winter (especially early winter) and does not show either a November peak or a January dip in PDO influence, as indicated by the monthly charts.  It's not necessarily surprising that daily probabilities behave very differently from monthly probabilities, but I'll have to think some more about possible explanations for the difference.  Interestingly the annual peak in probability for positive temperature anomalies with the positive PDO phase falls at the end of April, and the annual minimum is less than a month later; however, the median temperature is always above normal.

The daily chart for the negative PDO clearly shows the peak in negative PDO influence in November, but then there is a fascinating spike up in December, and the median temperature anomaly is above zero on about December 20.  It would be interesting to look at the historical years in more detail to see how this plays out; I suspect it is a reliable feature of the subseasonal evolution in the wake of a cold PDO-induced trough over Alaska in November.

It's also interesting to note that daily temperatures are more likely to be above normal than below normal in most of June, August, and September during the negative PDO phase.


  1. Are we taken care that an outlining year doesn't overwhelm the signal? How would removing the sudden warm up of spring 2013 or the falling strange winter before change things?

    I also read the first chart as saying that as the PDO anomoly increases so does the temperature anomaly. Would this be true? Or is the winter temp variation fairly stable despite the PDO?

    I think we need an analog forecast based on current conditions. How cold is it going to get next month?

    1. Eric, there is obviously some sampling noise in the daily charts, but the sample is fairly large (and I looked at median, not mean) so will not be dominated by a single extreme year. I'll try to show this later by looking at the December spike in temperatures for negative PDO.

      In general I would expect larger PDO anomalies to have larger effects on temperature, so the major influences shown in the charts should show up more reliably and/or strongly when the PDO index is large in magnitude. One could look at the more extreme PDO cases separately, but of course the sample size gets smaller...

      Good question on the analog outlook for January; I'll see if I can pull out some similar years and find anything other than "warm" as a forecast.

    2. Thanks Richard. In the last year plus that I've been following this blog, I've learnt a thing or two about using proper statistics, ie median is usually more stable than mean. There has been too much bad science because of the use of bad stats. Luckily, you seem to get it right. :)

      I've long noticed that there is a warming in the record lows of December as compared to November and January. Your graphs suggest that a weak PDO brought those on so now I have a more detailed reason for such behavior. I'll be waiting for the digging into of that Dec spike.

  2. I need new glasses but are the top and bottom Quartile ID's reversed in Fig. 4?

    Very nice examination Richard. But you know me, I have to ask how cloud cover and warm/cold advection relate to + and - PDO's, especially in winter. In summer the reverse may be true...clouds cool and advection may upset the insolation-induced temp stratification.

    Back when, the Professor would suggest ANOVA class analyses and the class would groan. I'm not the Professor.


    1. Gary, I think Figure 4 is OK - for negative PDO, winter temperature anomalies are usually negative (black line, left axis) and the probability of warmth is low (blue line, right axis). Click on the chart for a larger version. Let me know if you still think it's wrong.

      Interesting point on clouds: if the negative PDO causes reduced cloud cover year-round, this would favor warming in the summer when rates of advection are small. But the positive PDO is also warm in summer. As you suggest, the joint distribution of PDO/clouds and PDO/advection would be instructive.

    2. Still confused. Not about the thin Upper/Lower Quartile Temperature Anomaly range lines, but the labeling of the Top/Bottom Quartile heavy lines. Seems intuitive the Top should be Red; the Bottom Blue. Maybe a good switching in front of the class is in order, followed by me standing in the corner. Been there so no problem.

      Summer versus winter versus PDO. I suspect that insolation and advection (or the lack of) have a more pronounced effect than clouds in determining summer temperatures in Interior Alaska. Without an examination of seasonal cloud cover versus phase of the PDO it's just an assumption. That's where a model of the joint distributions you suggest would be instructive.


    3. Got it Gary! With Brian's help I realized that I was inexplicably looking at Figure 6 rather than Figure 4. I most certainly deserve the switching for wasting your time. Thanks for persevering.