Friday, December 10, 2010

A glance at model variability

In an earlier post I used the power of ensemble modeling to look at a forecast snow event for the upper midwest.  Well, it turns out that this weekend another Alberta-clipper-like cyclone is forecast to sweep across the upper midwest and could bring heavy snowfall to some places.  Earlier in the week much was being made of the "uncertainty" with regards to this event.  Claims were being made that the models were just all over the place.  But how much do models really vary?  Sure it makes sense that long-range models going out beyond a week in advance can vary a lot, but what about only 3-4 days in advance?  Shouldn't we have a good idea what's going on?

Let's use the SPC Short-Range Ensemble Forecast (SREF) system again to take a look at this question with regards to the upcoming snow event in the upper midwest.  We can measure the "variability" in the models by looking at the standard deviations (the "spread") between different models and how that changes over time.

First, here's the current SREF image for a 36 hour forecast of 700 mb heights.  This would be forecast to occur at 21Z this Saturday--sometime Saturday afternoon.
Fig 1 -- SREF 700mb mean height and standard deviation (shaded) in a 36 hour forecast for 21Z, Saturday, Dec. 11, 2010. From the SREF website.
This contours represent the average geopotential height field from all of the ensemble model members at this time.  This shows a relatively well-developed cut-off 700mb low-height center over northeastern Iowa.  I used the 700mb map because in a lot of winter weather events, the center of the heaviest band of snow tends to follow the track of the 700mb low (not always, but often).  Anyhow, the shaded areas represent places where there was more disagreement between the models (higher standard deviations).  You can see that the entire center of the cut-off cyclone seems to be in the area of uncertainty.  However, these standard deviations are at the lowest shading possible--only 20-30 meters as a standard deviation of height variations in that area.  Generally not too bad.  Now this is from 36 hours out. What did things look like from 84 hours out--two days earlier?
Fig 2 -- SREF 700mb mean height and standard deviation (shaded) in an 84 hour forecast for 21Z, Saturday, Dec. 11, 2010. From the SREF website.
Let's start by looking at the mean height fields themselves.  Immediately noticeable is how at 84 hours out, the 700mb low-height center is NOT cut off in this image--it's still forecast as an open-wave trough (in the ensemble mean).  In terms of placement, the trough axis is still in about the same general place (focus on the purple height contous and not the standard deviation contours)--through central Wisconsin and into northeastern Iowa. However, the trough itself seems much broader in the 36 hour forecast than in the 84 hour forecast.  Obviously the standard deviation is much higher in the 84 hour forecast than in the 36 hour forecast--from 84 hours there was a maximum standard deviation of 40-50 meters in height.  That's a lot of ambiguity about the strength of this trough, particularly since the highest standard deviations are right in the center of the trough.  This makes me think that some of the models were cutting off the trough and others were leaving it open.  The mean of all of the models still happened to be an open wave, though.

For an animation of how this 700mb map changed between an 84-hour forecast and the current 36 hour forecast, you can go to this animation here. It's by looking at sequences of images like this that we can identify "trends" in the models.  Based on that animation, here are three quick trends that I spot:
  1. The center of the trough axis (or cut-off low-height center) does seem to be subtlely moving westward and slightly further north as model runs got closer to the actual time.  It was difficult to really see this in comparing the first and last images, but in looking at the animation, this does seem to be the case.
  2. As each model run got closer, the strength of the 700mb cut-off low (based on the lowest minimum height and the number of contours surrounding it) has definitely been increasing--the closer we get, the more intense the models seem to be making this storm.
  3. The standard deviation tends to decrease the closer we get to that forecast time--this is what we expect.  Smaller standard deviations indicate better agreement between the models and more confidence in the overall forecast.  So whereas two days ago it was made a lot of sense for forecasters to be talking about so much "uncertainty", now things are coming into better agreement and we're drawing stronger conclusions.
We can look at other "variables" to also look at model spread. For instance, we could do an objective analysis on each model's surface pressure field to pick out where the surface low-pressure centers are.  Then we could plot where each ensemble member model said that the low pressure centers were.  Such a plot for the current 36 hour forecast is shown below.
Fig 3 -- SREF Surface low pressure center "spread" in a 36 hour forecast for 21Z, Saturday, Dec. 11, 2010.  From the SREF website.
In the above image, we can see that the low pressure centers tend to cluster--this is good.  It shows that all the models have somewhat of a good agreement on where the low should be.  The different colors correspond to different ensemble model members, so they don't indicate anything about confidence.  There's still some spread in the low center positions, as some have the low center in central Wisconsin and others have the low center in northeastern Iowa, but still--pretty good agreement.  Compare this to the same map, but for our 84 hour forecast:
Fig 4 -- SREF Surface low pressure center "spread" in an 84 hour forecast for 21Z, Saturday, Dec. 11, 2010.  From the SREF website.
Wow--what a spread between the low pressure centers!  None of the models placed a surface low in Wisconsin or Iowa.  They're scattered all the way from Texarkana up through central Illinois.  With lots of variability in the location here, there's very low confidence.  Also, based on our 700mb mean height field at 84 hours from above (figure 2), not many of those low center places seem to be likely spots for a surface low, anyhow.  The main trough (and upper-air support) on the 700mb map would be further north than any of these low centers.  So by remembering continuity between different variables and structures in the atmosphere, we can add our own element of educated awareness in interpreting model output.  If our surface results don't seem quite consistent with our upper air results, we really must question the accuracy of the models.

Like before, here is an animation of how the surface low centers map evolved from the 84 hour forecast to the current 36 hour forecast.  We see that the low centers quickly began to accumulate further north and then slowly have been retreating westward to the close cluster that they are currently.  We've seen slow westward retreats in both the surface lows and the 700 mb map--both of these point to the models thinking the cyclone is going to move through later and later, moving more slowly than previously thought. 

We can keep trends like that in mind when looking to future runs as well.  You might guess that as we get closer and closer to this event, the models may continue this slowing trend and the timing of the forecast will change.  However, also remember that the closer we get to the time, the more the model "spread" or standard deviation tends to decrease. As the models come into better agreement and are more confident on a solution, that particular solution may not change as much as it used to at earlier forecast times.  So while we may still see that slowing of the progression of this cyclone, it may not slow down in future model runs nearly as much as it has been.

Finally, I STRONGLY encourage you to explore the SPC's SREF website.  They have ensemble graphics for nearly any variable imaginable.  Also, if you're viewing a particular image at a particular forecast time and want to see what previous model runs said for that time (like I did above), just click on the forecast hour number (f36, for example) for the image at the time you want and it will load up all the model forecasts for that time from all the previous runs.  Have fun!

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