A few days ago I thought it would be interesting to see what would happen when calculating what day of the week was the warmest in the U.S. It was intended to be a silly exercise to demonstrate that even if one day was the highest it would be statistically trivial. I looked at 'primary' stations only since my poor computer could only handle two years at once before crashing. So I queried 2012 and 2013. Well, much to my surprise, there were very distinct patterns. Not only were the patterns geographical, but the were temporal and propagated from west to east. Figure 1 shows the warmest days of the week for all primary stations in the U.S. Across areas with minimal longitudinal variation, the daily percentages are staggeringly variable. In Alaska for example (see Figure 2), an amazing 41% of stations were warmest on Thursday and only 4% are warmest on Tuesday or Wednesday. To me, that is a signal indicating a possible climate connection.

I then set out to check time periods other than seven days. Of course a seven day period corresponds very nicely with a calendar week. I checked time periods between 2 and 30 days. For the 30-day period think of it as grouping Jan 1, Feb 1, March 1, etc. and calling those "Group 1". Then take Jan 2, Feb 2 March 2, etc. and call those "Group 2".

After a little trial and error, it was pretty obvious that 4-days was a very prominent pattern for the Lower 48 and modestly prominent for Alaska. Figure 3 shows which of the repeating 4 days is the warmest for the Lower 48 and Figure 4 shows the same but for Alaska.

Fig 3. All primary stations in the U.S. mapped according to which day, of a repeating 4-day pattern, during 2012 and 2013 was the warmest. Only stations with 95% complete data were used.

Fig 4. All primary and RAWS stations in Alaska mapped according to which day, of a repeating 4-day pattern, during 2012 and 2013 was the warmest. Only stations with 90% complete data were used.

Looking at the ESRL Reanalysis data (see Figures 5, 6, 7, and 8 below), a very clearly defined 4-day thermal wave is evident. I compared each of the four repeating days with the other days in the 4-day set to track the atmospheric patterns for 2012 and 2013. I am quite amazed that given the number of days used in the analysis (728) that any pattern whatsoever holds up. If the 4-day pattern was 3.5 or 4.5 days it would break down in the reanalysis data after a while. When I ran the same analysis at the 7-day interval (not shown) a noticeable, but less prominent thermal wave was also evident. I can share those images with anyone who may be interested.

So what recurs at 4 and 7 days. One obvious answer is planetary (Rossby) waves. They tend to recur at 7-day intervals according to the literature but their period is pretty variable and is highly dependent on the number of waves. The fact that the 7-day pattern in Figure 1 is more prominent between 40°N and 50°N lends credence to the planetary wave origin for that length time period. But what about the 4-day pattern? It has a much stronger signal. Is it related to planetary waves? What drives the thermal push depicted in Figures 5-8? Also, might the 7-day pattern actually be a 1/2 strength version of the 4-day pattern since 7 is almost, but not exactly, a multiple of 4?

Surely this is not a new discovery. My brief search of the literature didn't lead to any obvious answers beyond the Rossby wave solution.

Looking at the ESRL Reanalysis data (see Figures 5, 6, 7, and 8 below), a very clearly defined 4-day thermal wave is evident. I compared each of the four repeating days with the other days in the 4-day set to track the atmospheric patterns for 2012 and 2013. I am quite amazed that given the number of days used in the analysis (728) that any pattern whatsoever holds up. If the 4-day pattern was 3.5 or 4.5 days it would break down in the reanalysis data after a while. When I ran the same analysis at the 7-day interval (not shown) a noticeable, but less prominent thermal wave was also evident. I can share those images with anyone who may be interested.

So what recurs at 4 and 7 days. One obvious answer is planetary (Rossby) waves. They tend to recur at 7-day intervals according to the literature but their period is pretty variable and is highly dependent on the number of waves. The fact that the 7-day pattern in Figure 1 is more prominent between 40°N and 50°N lends credence to the planetary wave origin for that length time period. But what about the 4-day pattern? It has a much stronger signal. Is it related to planetary waves? What drives the thermal push depicted in Figures 5-8? Also, might the 7-day pattern actually be a 1/2 strength version of the 4-day pattern since 7 is almost, but not exactly, a multiple of 4?

Surely this is not a new discovery. My brief search of the literature didn't lead to any obvious answers beyond the Rossby wave solution.

**Any ideas would be much appreciated**.
Fig 5. Day 1 of the 4-day thermal wave as depicted by the ESRL daily composite reanalysis. A wave axis is superimposed as a red line. This is a compilation of all Day 1s minus the average of Days 2, 3, and 4. 728 days were used in the analysis.

Fig 8. Day 4 of the 4-day thermal wave as depicted by the ESRL daily composite reanalysis. A wave axis is superimposed as a red line. This is a compilation of all Day 4s minus the average of Days 1, 2, and 3. 728 days were used in the analysis.

* Update section

After reading a section from a paper from 1976 (Blackmon, M. L. 1976. A climatological spectral study of the 500 mb geopotential height of the Northern Hemisphere. J. Atmos. Sci. 33, 1607 -1623.) that describes the propagation period of Rossby waves as 20° longitude per day, I decided to make reanalysis plots of the 500 mb height anomalies. The 20° value corresponds to 1/4 of the width of the Lower 48 states. Therefore, the 4-day thermal wave may be entirely explained by that.The wave train of anomalies stands out very nicely and clearly propagate from west to east.

Fig 9. 500mb height anomaly on Day 1 of the 4-day thermal wave as depicted by the ESRL daily composite reanalysis. This is a compilation of all Day 1s minus the average of Days 2, 3, and 4. 728 days were used in the analysis.

Fig 10. 500mb height anomaly on Day 2 of the 4-day thermal wave as depicted by the ESRL daily composite reanalysis. This is a compilation of all Day 2s minus the average of Days 1, 3, and 4. 728 days were used in the analysis.

Fig 11. 500mb height anomaly on Day 3 of the 4-day thermal wave as depicted by the ESRL daily composite reanalysis. This is a compilation of all Day 3s minus the average of Days 1, 2, and 4. 728 days were used in the analysis.

Fig 12. 500mb height anomaly on Day 4 of the 4-day thermal wave as depicted by the ESRL daily composite reanalysis. This is a compilation of all Day 4s minus the average of Days 1, 2, and 3. 728 days were used in the analysis.

Fig 11. 500mb height anomaly on Day 3 of the 4-day thermal wave as depicted by the ESRL daily composite reanalysis. This is a compilation of all Day 3s minus the average of Days 1, 2, and 4. 728 days were used in the analysis.

Fig 12. 500mb height anomaly on Day 4 of the 4-day thermal wave as depicted by the ESRL daily composite reanalysis. This is a compilation of all Day 4s minus the average of Days 1, 2, and 3. 728 days were used in the analysis.

A few thoughts. It seems that a quick review of the research (via Google) shows 5 day waves - not 4. But since you feel that the data is robust why would this be different?

ReplyDeleteThe more "extreme" weather lately has been attributed to a more variable jet stream. Would thus varibility affect the wave's speed enough to make 4 days?

Here in Fairbanks, from Nov 2012 - Jun 2013, there was a very consistent pattern of 28 days warm and then 28 days cold repeating. Is this related to the 7 day wave?

I remember some years ago reading a news article that claimed that it rained more on the weekends. They said it was most likely due to increases in particulates. I didn't buy that. I don't remember what cities they used, but if they were on the east coast then the rainy warmth would be on the weekend according to what you found. I would believe that more.

Remember that monsoon season is upon the southwest during July and August of each year. That would cause chaos.

Thanks Eric. After a little more research this morning, I found a paper that describes the eastward propagation of Rossby waves of 20° per day (http://kiwi.atmos.colostate.edu/group/dave/at605pdf/Chapter_8.pdf). That corresponds to 1000 km per day at 40°N latitude. Since the west-east distance of the Lower 48 is about 4,000 km, the 4-day thermal wave might be entirely explained by Rossby waves.

DeleteBrian,

ReplyDeleteInteresting work - well done. I was aware of a 7-day periodicity; the 4-day wave is new to me, although it makes sense. However, I am still surprised that the pattern holds up for two full years - I would have wagered that the waves would get out of phase pretty quickly and cause the signal to wash out, e.g. Day 1 on the beginning count quickly becomes Day 2 or 4 after a phase shift. The question is, how long does the phase stay in sync? Is something anchoring the 4-day wave phase? All very curious...

This kind of stuff makes my brain hurt. I came across these Waves last year via the CPC's webpage and reading about their use of Rossby Waves, Wave Packet analyses, and Baroclinicity. Search there for more links. I know more than I understand about this.

ReplyDeleteGood analyses Brian. I suspect one might have to back it up into Eurasia (to look for possible Anthropogenic forcing), or worldwide to see if it's a circum-global phenomenon.

Gary

Richard, I tend to agree with you. Even a strong signal will break down over time unless its tendency to drift to a long term mean, and in this case a whole number) is very strong. On one hand this all seems like a statistical fluke. On the other hand, where there's smoke there's often fire. We'll see. I'm all for getting as many second opinions as possible. I'll do some more reanalysis next week. ESRL only allows you to enter 1000 or fewer days to run the numbers.

ReplyDeleteGary, it made my head hurt too. I spent several nights last week working on this from after my kids' bedtime until midnight. There are lots of combinations and permutations.

Staring at the 500 mb figures, I've noticed that there is three clear regimes present from about 0 - 30º, 30 - 60º and 60 - 90º. This looks like three different air masses. Which makes sense since the waves would be a composite of the polar and tropical jets - which are Rossby waves.

ReplyDeleteIt also becomes clear that the northern latitude sequence has a lower number and the tropical region is weak. This makes me suspect that the 4 day signal is created by the latitude but sustained by resonance within the middle continental air mass.

Of course this is speculation and I'm not going to dive into the world of wave numbers. While I really like this field of study, I don't have time right now.