How confident are we in snow for the upper midwest?

A swath from central Minnesota through Wisconsin, northern Iowa and into northern Illinois is expected to get some fairly significant snowfall starting Friday afternoon and into Saturday morning.  The National Weather Service is already putting out winter storm watches for much of the area.

But, if you live in the midwest, you know--we've heard this before.  Predictions of over half a foot of snow that don't materialize or completely missing a huge snowfall until it's too late.  Now, taking a look at model forecasts aloft over the next few days, it doesn't look very impressive.  Here's what this morning's GFS run shows at 500 mb on Friday evening:

Fig 1 -- 36 hour GFS forecast of 500 mb geopotential heights and winds for 00Z, Sat. Dec. 4, 2010. From the HOOT website.

No majorly-impressive trough diving across the plains or anything like that.  Only a very subtle shortwave over the eastern Dakotas accompanied by a wind maximum aloft.  If we apply our jet-streak-divergence-aloft dynamics, we might expect there to be enhanced surface cyclogenesis in the Sioux City, SD area and look for our surface low to be centered around there (we'll see later if this agrees with the model).  Remember from our thermal wind arguments in my previous blog posts that jets tend to form over temperature gradients below.  As such, we would expect colder air to the north of the jet and warmer air to the south.  Since clearly the main axis of these jets is to the south of the upper midwest, we would expect the upper midwest to be on the colder side of the jet--good for snow.

In another blog post I talked about using critical thickness values to help determine where snow would fall.  Here's a view of the GFS forecast for most of the major critical thickness lines for Friday evening:

Fig 2 -- 36 hour GFS forecast of critical thickness lines for various heights (exact parameters not shown) for 00Z, Sat. Dec. 4, 2010.

Note that the same region of Minnesota, Wisconsin and northern Illinois is north of all the critical thickness values, indicating that the atmosphere should be cold enough to support all snow.  That is, according to the GFS model.  If we quickly look at the GFS surface prediction:

Fig 3 -- 36 hour GFS forecast of surface temperature (shaded), sea-level pressure (contoured) and winds for 00Z, Sat. Dec. 4, 2010.  From the HOOT website.

Remember how the upper air pattern seemed to favor a low forming in southeastern South Dakota?  It's not that well represented in the contoured pressure field here.  If you were to look only at those contours, you'd suspect a low somewhere in the Oklahoma panhandle.  But, note how the winds do have a counter-clockwise sort of swirl in southeastern South Dakota, and there is a trough in the pressure field that bulges up in that direction.  Still--not the greatest organization at the surface.

Now that's just one model.  We're close enough to this event that we can look at medium-range models as well.  Let's look at the NAM forecast for this same time.  Here's the 500 mb chart:

Fig 4 -- 36 hour forecast of 500 mb geopotential height and winds for 00Z, Sat. Dec 4, 2010.  From the HOOT website.

Our jet streak looks really different here.  In fact, it looks more like two jet streaks.  Whereas the GFS 500 mb forecast above had a single jet streak centered over Nebraska, the NAM here has two jet streaks--one centered over central Wyoming and another centered over Colorado.  Both of these are 36 hour forecasts for the exact same time for two different models.  Quite the difference, though.  The shortwave is not very well-defined at all on the NAM, and the NAM also seems to be bringing these jet streaks through much more slowly.  Of additional concern--if the northerly jet were to be favored in the NAM solution, we night expect that boundary between the colder air and the warmer air to be further north--meaning our rain-snow line would push further north.  Concerns abound here...

We could look at more model graphics for both of these models and try to reconcile them with each other.  But we know that both models have their flaws and we could agonize for hours trying to answer a simple question--is it going to snow or not?  What if we could somehow look at lots of models with their slightly different solutions all at the same time to see if we can make any general conclusions about where the models do agree?  But wait--we can do this!  Through the use of model ensembles.

The basic idea is this.  We know that the GFS, NAM or any other model is flawed in many ways.  There's also errors in the data we used to initialize the model in the first place.  But generally, the models do capture the general flow of things quite well.  So what if we ran the same model several different times, using slightly different initial conditions each time, and then seeing how many of those model runs agreed on some particular parameter?  People are doing this in research groups across the country. For example, NCEP runs a GFS ensemble at the same time as the operational GFS model (the one we always look at).  They run 20 GFS models all with slightly different initial conditions.  As a result, we can get plots like this:

Fig 5 -- GFS ensemble 500 mb geopotential height enemble mean and normalized ensemble spread for a 36 hour forecast valid 00Z, Sat. Dec. 2, 2010.  From the NCEP EMC website.

This graphic shows the average 500 mb heights (the black contours) between all 20 versions of the GFS that were run.  The color shadings indicate the degree of "spread" between the models--how much difference there was between each individual model that was run.  If all the models agreed on the same 500 mb height at a point, the spread there would be small.  If they disagreed by a lot, the spread would be higher.  The map above shows the entire northern hemisphere with the US toward the bottom.  If you look closely, you can see our subtle little shortwave trough over the Dakotas--it's still there in the ensemble mean.  However, note that the shadings in that area are in the yellows and reds.  According to the color scale, this means that there was high ensemble spread in that area--the models differed a lot in what 500 mb height they computed for that area.  This means that the GFS model really doesn't have a good handle on what's going on there, as slight perturbations seem to have caused great differences in the 500 mb height across the models.  Even though we still see a shortwave there in the mean, we're not as confident in its structure.

However, we can do this sort of analysis for any parameter we want.  So what question were we asking?  Are we going to get snow from Friday into Saturday in the upper midwest?

Fig 6 -- GFS ensemble probability of precipitation exceeding 0.1, 0.25, 0.5 and 1.0 inch in a 24-hour period between 12Z Dec 3, 2010 and 12Z, Dec 4, 2010. From the ensemble initialized at 00Z, Dec 2, 2010.  From the NCEP EMC website.

I apologize for this series of maps being so small.  Clicking on it should make it bigger (though I still think they're small).  This series of maps has a simple concept that's slightly difficult to explain.  Each of these maps shows the probability, according to the ensemble, that precipitation will exceed a certain amount over a 24 hour period between Friday morning and Saturday morning.  How was this probability calculated?  I'm assuming (though I haven't verified this in their documentation) that, for instance, in the first panel of the above image where the threshold is 0.1 inches, if 90% of the ensemble models said there would be at least 0.1 inches during that time period at a point, then that's where the 90% probability came from.  So this probability is essentially the percent of the models that say that this is going to happen.

We can see in the image above that for much of that swath from Minnesota through northern Illinois, there is at least a 70% (if not higher) probability of at least 0.1 inches of liquid equivalent precipitation from Friday morning through Saturday morning.  There's even a good-sized area of greater than 60% chance of at least 0.25 inches of liquid equivalent precipitation in that are as well.  So even though the GFS doesn't have that great of a hold on this system, the majority of the models show that precipitation will fall in that area.

There are other ensembles we can look at too.  For instance, the Storm Prediction Center runs what's called the SREF -- Short Range Ensemble Forecast system. It's basically an ensemble of WRF models that are analyzed in the same way as the GFS ensemble.  So what do they say about precipitation?

Fig 7 -- SREF probability of 24-hour liquid equivalent precipitation greater than 0.1 inch ending at 12Z, Sat. Nov 4, 2010.

I like these bigger graphics better.  You can see that the SREF has a huge swath from northern Illinois up through eastern North Dakota with a greater than 90% probability of greater than 0.1 inches of precipitation from Friday morning to Saturday morning.  That's pretty confident.

Fig 8 -- SREF probability of 24-hour liquid equivalent precipitation greater than 0.25 inch ending at 12Z, Sat. Nov 4, 2010.

There's still a large swath in that same area where the probability of more than a quarter of an inch is greater than 70%.  Still pretty high confidence here.

Fig 9 -- SREF probability of 24-hour liquid equivalent precipitation greater than 0.5 inch ending at 12Z, Sat. Nov 4, 2010.

By the time we get up to half an inch, though, the probabilities have dropped considerably--only 50% at best.  So based on this, we'd conclude that there's a high probability (according to the WRF model ensemble here) of seeing liquid equivalent precipitation values of between 0.25-0.5 inch through much of that swath from North Dakota down through northern Illinois.

So what does this all mean?  Even though we looked at two different model environments (GFS and WRF) (the NAM model is actually a WRF model now, so it enhances our comparison even further...) that had low confidence and differences in the upper air patterns and surface low placement and all that, surprisingly they all agree to a decently high probability that much of that geographical swath will see a good amount of liquid equivalent precipitation.  Not bad for pulling something conclusive out of inconclusive models...

Still...how much snow does this mean?  I am going to write a blog post soon where I look at different methods of calculating snow amounts from liquid equivalences.  For now, a general rule of thumb often used is the 10:1 snow ration--10 inches of snow for every 1 inch of liquid water equivalent.  Applying that to what we saw above, our 0.25-0.5 inch range of liquid equivalent would translate to 2.5-5 inches of snow.

I didn't really stop here (beyond the quick check of critical thickness) to look at if this precipitation would all fall as snow--remember, there was that concern that the critical thickness lines could come north if the jet stream stayed further north.  Based on my quick look through the models (more than I showed here), they actually all seem to be keeping the low to the south and keeping that precipitation swath well in the colder air.

So, in conclusion, I see where the NWS snow forecasts are coming from based on the power of model ensembles.  Ensembles hold great promise for the future of weather prediction--I'm sure I'll be writing more about them in the time to come.

***Update***

As many people have pointed out to me over the last hour or so, the SREF page has a whole section of ensemble products devoted to probabilities of winter weather.  As such, we can see far more detailed predictions instead of just the liquid equivalent.  I used the liquid equivalent because that was available in both the SREF and the GFS ensemble and so I could compare them.  But, by popular demand, here are three SREF snowfall predictions:

Fig 9 -- SREF most probable precipitation type for 12Z, Sat. Dec 4, 2010.  45 hour forecast.

The above figure uses an algorithm developed by NCEP to try and pick what is the most likely precipitation type in each model.  If a majority of models support a certain precipitation type, then that's the type that appears on this image.  The solid red line is the mean location of the 32 degree Fahrenheit isotherm among all ensemble members.  You can see that the entire upper midwest is in the blue, representing snow.

Fig 9 -- SREF probability of snowfall for 12Z, Sat. Dec 4, 2010.  45 hour forecast.

This image is a combination of the probability of precipitation and the probability of precipitation type images.  It's basically probability that there will be snow falling on Sunday morning at each point.  You can see much of southern Wisconsin has a 90% probability of snow falling on Sunday morning.

Fig 9 -- SREF previous 12 hour snow accumulation for 12Z, Sat. Dec 4, 2010.  45 hour forecast.

And finally this is the ensemble mean for how much snow will accumulate over a 12 hour period from Friday evening through Saturday morning.  You can see that the average in all the models has a maximum of 4-5 inches in the Mississippi River valley on the Minnesota-Wisconsin border.  But this is just as of early Saturday morning.  We saw in the above two images that snow was projected to be falling at that time across southern Wisconsin and northern Illinois.  Thus, if you look at later images, more snow is added further south.