Monday, January 27, 2014

Questioning the Bering Sea Rule: Part 1

Minor correction:  in the first version of this post, I described some of the bloggers who initially developed this rule as employees of Accuweather.   I've been informed that this is not actually the case, so I removed the Accuweather forecaster references.

In the craziness of all these meteorologists now posting forecasts on the internet, I've been impressed with how thorough and creative several of these individuals are at presenting weather information in new, detailed and informative ways.  Every so often, though, there's something that comes up that just bothers me to no end until I've dug into it some more.  This (somewhat long) blog post will describe one of these forecasting curiosities--something termed the "Bering Sea Rule".

There are a small group of forecasters out there who hold great faith in this rule for issuing general weather predictions for the eastern US 2.5-3 weeks in advance--pushing the very edges of the limit of predictability for specific atmospheric patterns (predicting the mean state of the atmosphere has much longer limits...but that's another topic).   The origin of this theory seems to come from a poster on an Accuweather blog, who posted a brief description at this link.  Other blogging forecasters also use this theory to issue their own multi-week/monthly forecasts.  Some examples are this blogthis blog and this blog.  Is there a coincidence with Accuweather's recent decision to start issuing 45 day forecasts that have virtually no skill?  I have no idea...

Before continuing, I want to get out of the way that many of these blogs are filled with good analysis of several of our long-range weather diagnostics.  I'm not criticizing these blog posters, I'm just curious about this Bering Sea Rule and if it has any validity.  So that's what I'm going to investigate here.

Let's start with what the "Bering Sea Rule" actually states.  The original description in that first link describes it as a casual observation by one forecaster that the blog poster later "correlated":
"...after some monster storms of 1950 and 1974 in the Bering Sea, that within 3 weeks of those storms we saw monster storms for the East...I have amassed multiple post where I have correlated the above to a pattern..."
Without any strong specifics as to what the rule is about.  Some of the other blogs I linked to above offer the following descriptions:
  • "Bering Sea Rule (BSR): ...The basis of this theory is that whatever is occurring in the Bering Sea can be expected in the eastern CONUS within 2.5-3 weeks of its occurrence in the Bering Sea. Simple as that." (source here)
  • "The Bering Sea Rule states that by watching storm systems make their way across the Bering Sea, one can identify where and when a storm system will show up in the United States. The general timeframe is 17-21 days after a storm appears in the Bering Sea, a storm will appear in the United States." (source here)
Other claims throughout the blogs I listed describe how the Bering Sea Rule is "independent of season" and another blog (located here) tries to use this rule (or a modified form of it) to correlate western Bering Sea/Kamchatka pressure to mean temperatures in the Midwest.

So is there anything to this rule?  Can we use what's happening in the Bering Sea to predict storminess and/or temperatures in the eastern US three weeks later?  I decided to do some correlations to see what I could find out.

To examine this, I'm using the European Centre for Medium-Range Weather Forecast's Interim Reanalysis (abbreviated ERA-Interim).  What does this "reanalysis" give us?  Basically they go back and do a detailed data assimilation of all available observations every six hours to get a "best guess" at what the full state of the atmosphere actually was at that time.  I'm going to use these reanalyses all the way from 1979-2010---that's 31 years of atmospheric states to look at. If there's a pattern we should be able to find it.

Next step--what regions are we going to use for the Bering Sea and the US?  One of the rule definitions above describes the US part of the rule as the "eastern CONUS", so I'm going to look at the US east of the Rockies.  For the Bering Sea, I'm not going to use the western Bering Sea/Kamchatka region defined by one of the blogs and instead use the entire Bering Sea as the area of interest.  This seems to be consistent with what most people are doing.  Here's a map outlining the two regions I'm going to use:

Ok.  We have a source of weather "data" (the reanalyses) and regions to focus on.  In theory, if there is any predictive power here, then the "storminess" of the Bering Sea should correlate positively with the "storminess" of the eastern US ~17-22 days later.  How do we define "storminess", though?  I'll try two possible ways (or "metrics"):
  • We can compute the average mean-sea-level pressure (MSLP) over the entire region (either Bering Sea or eastern US).  When the average MSLP is lower, it's more stormy.  When the average MSLP is higher, it's calmer.
  • We could instead look at the variance of MSLP across the entire region.  This is kind of a measure of the range of pressures spanned in the region.  If the entire area has exactly the same pressure (nothing interesting going on), the variance would be zero.  If a deep low is moving in (getting stormier), we would expect the variance to be higher.  This measure is often used in climate studies for identifying storm tracks.
On top of this, some of the bloggers using the Bering Sea Rule look at 500 hPa heights instead of we can also try the same three methods above using 500 hPa heights instead.  Finally, there was also that one blogger that was using the rule to try and track the mean temperature of the Midwest---I'll try correlating with the mean temperature in the eastern US region in part 2 of this blog post some time later.

Some final notes about the methodology---when computing these indices, I am going to remove the annual cycle by first computing the average value over the entire 30-year climatology for every day for each metric.  Our metrics will then be reduced to deviations from the mean value for each day.  For instance, instead of using the average MSLP over the Bering Sea for January 5th, 1984 I will use the difference between that value and the average MSLP over the Bering Sea for every January 5th from 1979-2010.  This will remove seasonal cycles of storminess.  Secondly, using 6-hourly data is a bit much for this kind of work--it's going to probably be very, very noisy.  Because of this, I'll smooth the timeseries out a bit by taking running averages over certain time length windows.  It's unclear what time length is best--should I take average values over the past day?  Over the past week?  Since it's unclear, I'll try doing this for a variety of averaging windows and see what we get.

All right.  Time for some results.  Let's start by correlating the mean Bering Sea pressure with the mean eastern US pressure at various lags (from 1-60 days later).  We're also going to use averaging windows ranging from correlating daily averages (1 day) to monthly averages (31 days).  Each colored line represents a different averaging window length.

So what do we see?  Notice as our averaging window gets longer (the different colored lines), the lag correlations become smoother and the correlation coefficient values increase (we're more highly correlated).  We reach a peak correlation of ~0.20 for long running mean windows (31 days) at a 7-day lead time.  This means that a "stormier" than normal Bering Sea over the last month is weakly correlated with a stormier than normal eastern US over the last month too, but about one week later.   Similar peaks (from 5-7 days lead time) exist for shorter averaging windows.  For instance, if we just take the average MSLP over the past day in the Bering Sea, lower than normal pressures over the past day very weakly correlate (~0.13) with lower than normal pressures over a one-day period in the eastern US ~5 days later. Not exactly the result we'd want under the Bering Sea Rule.  In fact, this corresponds reasonably well for the time period for shortwaves in mean mid-latitude westerly flow to propagate the distance from the Bering Sea to the eastern US.  I've highlighted the time period (17-23 days) when the Bering Sea Rule claims enhanced predictability with the green shaded region--there's no peak in correlation there. So this doesn't look so good.

Just for comparison, let's look at the self correlation of eastern US average mean-sea-level pressure for the same period.  This looks at the predictive power of the storminess in the eastern US right now for telling us how stormy it will be in the future.  Here's what that looks like:

For zero lead times, the correlations are all one (I actually didn't compute zero lag--started with 1-day lag--so they don't all go up to one on the left, but they would if I did).  This is what we expect--a timeseries should be perfectly correlated with itself.  But what about when we start lagging it?  If we look at the same lines as in the previous plots with the highest correlations (31 days averaging at a 7-day lead time), correlations are still at best ~0.2.  Those are the same as correlations to the Bering Sea, implying that you could actually predict the monthly average eastern US "storminess" 7 days from now just as well as the Bering Sea Rule could by looking at how stormy the eastern US has been over the last 31 days.   

For short averaging lengths (so, lower than normal pressure over the last day or week (1-11 days)) there actually is a tiny bit higher correlation to the Bering Sea at 10-20 days of lead time---but we're talking really small correlations here of 0.07 or less.  In our 17-23 day Bering Sea Rule window, the self-correlations rebound slightly, once again indicating that for that timeframe you could predict the mean pressure in the eastern US just as well by using the recent pressure in the eastern US as by using the pressure in the Bering Sea.

Let's try looking at 500 hPa heights instead---correlate the mean 500 hPa heights deviations over the Bering Sea with the mean 500 hPa deviations over the eastern US.  Here things get somewhat interesting looking...
There's a nice sinusoidal pattern going on here with a period of around 34 days.  Note that the magnitude of correlation is actually at most 0.05--those are really, really small correlations at best.  Furthermore, it just so happens that the period indicated by the Bering Sea rule--that 17-23 day window--is actually one of the times with the smallest predictability.  The correlations at that time are around zero regardless of what averaging window you use.  So, this implies that 500 hPa height means have NO predictive skill at all between the Bering Sea and eastern US for the time periods indicated by the Bering Sea rule.

SIDEBAR: It's interesting to note this odd 30-40 day periodicity in these correlations.  I talked about this with my friend/colleague Angel Adames here at the University of Washington and we agreed that this might be symptomatic of a wavetrain generated by the Madden-Julien Oscillation (MJO).  This oscillation is a tropical phenomenon/large scale convective enhancement that circles the globe at the equator every 30-40 days on average with variations in strength.  As this feature propagates around the globe, it can cause fluctuations in jet stream strength and position which in turn can lead to synoptic-scale wave patterns that propagate through mid-latitudes.  Angel has composited the average wintertime effect of the MJO on upper-level heights for the entire 30-40 day MJO cycle.  An animation of this is at this link.  You can see that the MJO induces a series of troughs and ridges that strengthen first over Alaska and the Bering Sea and later on in the eastern US.  This underlying cycle might explain the strong sinusoidal pattern in the lag correlations.  But again--these correlations are so weak--0.05 in magnitude at best--that this is not a major impact at all on what happens.  But it's interesting...

Let's switch to looking at variances now as another measure of "storminess".  Here's the correlation of the variance in Bering Sea mean-sea-level pressure to the variance in eastern US mean-sea-level pressure.
Again...not the strongest signal...for any lead time.  If anything, at longer lead times beyond ~5 days, the variance in MSLP in the Bering Sea is anticorrelated with the variance in MSLP in the eastern US---meaning a particularly "stormy" period in the Bering Sea actually, if anything, points to less "stormy" conditions 7-30 days later in the eastern US.  How about looking at 500 hPa variance?
An interesting pattern here--the magnitudes of the longer-range (20-50 day) lead times are actually a little larger in magnitude (around -0.13) than we see for shorter lead times.  Still really small magnitude--not significant.  Furthermore, again at these longer lead times the signals are anticorrelated, if anything.  What about our 2.5-3 week time purported by the Bering Sea rule?  Like we saw in the correlations of mean 500 hPa heights, this is actually a time when the correlation goes through zero--no connection at all is evident.

So what does all this mean?  Looking at 30 years of correlations at various lead times, with various averaging windows, and measuring storminess as both the mean and variance of MSLP and 500 hPa heights in the Bering Sea and the eastern US, I can't find any good evidence at all pointing to a particular connection between storminess in the Bering Sea now and storminess in the eastern US 2.5-3 weeks later.  If anything, that lead time is in one of the worst times for predictability by these metrics.  If we looked at 1-2 weeks of lead time, maybe we'd have a slightly better case for a very mild predictability based on the 500 hPa mean heights and variance.  But those are still very small correlations...

That wraps up part 1 on this topic.  In a later blog post, I'm going to investigate this again in a little more detail.  I haven't shown the correlations to eastern US temperature at all, which is another feature that some have tried to predict using the Bering Sea rule.  Additionally, I noted that most of these Bering Sea rule comments began last autumn and have continued through the beginning of this year.  The last several months have been marked by an extraordinarily persistent pattern of ridging in the eastern Pacific/western US and troughing in the eastern US.  Perhaps this rule has more merit when the large scale flow is persistently in that pattern?  We'll test that one too.

Also, I welcome any and all comments on this!  Particularly for some suggestions of better metrics to check or other ways to approach this.


  1. I have been thinking about this, I think your first 7-day lag peak might be related to group velocity dispersion of low-frequency Rossby waves associated with the Pacific-North American (PNA) pattern, because it roughly represents all occurrences of the PNA, you might expect that correlation to be bigger than the one associated with the MJO. However, all low frequency waves will disperse their energy around in a couple of days so that 3 week relation will still be "misterious".

  2. I am also in the mode of proving the BSR with numbers. I have been following a mystical cycle myself for a few years called the LRC. It is evident that there is science to the magic. Translating ISO/MJO to the mid latitudes gives the recurring Rossby Wave Train some gusto. The BSR is a snap shot of the wave train, but the way Joe Renken is utilizing it is a bit different. Or is it? I am eager to reread your analysis and to potentially help assist.

    Some of my work can be found by visiting the link below.

  3. I appreciate the research that you have performed on this and look forward to future research to be compared to what the University of Missouri Atmospheric Sciences department comes up with!