Monday, February 21, 2011

Do snow ratios always increase when the temperature decreases?

On February 8, 2011, we Normanites were facing the prospects of a big snowfall forecast according to some model runs.  At least the kind that threatened to shut down the city for the rest of the week.  This would've meant all the workshop students that arrived here to take the final part of our course would be stuck in a hotel for days as Norman would've struggled to recover from the second major snow storm in two weeks.  For several days, the Short Range Ensemble Forecast (SREF) depicted anywhere from 6 to 18" of snow overnight Tuesday into Wednesday morning (see an example in figure 1).  Needless to say this kind of forecast should demand a lot of scrutiny simply because these amounts are so rare.  After the event was over, we found even the most conservative trace here to greatly overestimate what actually happened.  I only measured 2.7" of snowfall and the most I saw in central Oklahoma 5".  Needless to say I was disappointed because I love to see huge dumps.  On the other hand this event is an educational experience and I'll show you why.
Figure 1  SREF ensemble forecast of snow fall in Norman, OK from Wednesday 2011-02-08 21 UTC.  The snow fall forecast was based on a snow ratio technique dependent on surface temperature.  The most conservative forecast in this picture was 8".  The highlighted member (bright white) comes from the KF version of the WRF model using the ARW core with a snow depth of nearly 15".  See for details.
Stepping back to the big picture, this event was courtesy of a fast moving and elongated upper-level trough coming out of the southern Rockies phasing with the passage of an unusually intense arctic front dropping south.  The upper-level wave was not particularly deep and its track was further north than what we typically see with winter storms in Central Oklahoma.

The upper-level wave is depicted by the red shaded regions of strong 400-250 mb potential vorticity with the center in northern NM in this SPC mesoanalysis image taken at 0345 UTC 09 Feb 2011.  The blue contours show good potential vorticity advection already over much of the southern Plains into southeastern KS.
The strong arctic front surging into the southern Plains helped bring the strong lift further south and as a result, a large band of precipitation broke out from northeastern NM to central KS during the day Tuesday.  This band sank to the south and strengthened as the upper-level wave approached.  The strength of the frontal lifting was quite remarkable, especially in west Texas where the band started.  Take a look at this frontogenesis image below.  The 850 mb frontogenesis in southwest TX was so strong that the SPC mesoanalysis page ran out of contours.  Now at the elevation of the high plains, we're really looking at the surface front.  However, this frontal boundary deepened, and it probably featured bands of locally more intense lifting at higher elevations and helped to determine the location of the snow band.  Just to appreciate how intense this front was, look at the temperature contrast between Pecos, TX at 82 deg F and Clovis, NM to the north by 150 mi at 9 deg F.  Where else in the world do you get fronts like that?

The sharp arctic front depicted by the 850 mb frontogenesis in this SPC analysis at 02 UTC 09 Feb 2011.  I'll put this down as one of the all-star fronts.

Surface plot courtesy of NCAR/RAP for 2233 UTC 08 Feb 2011.  The front features a contrast from 82 deg F at Pecos, TX to 9 deg F in Clovis, NM.

Certainly the forcing for vertical motion aloft phasing with extremely cold surface air would lend credence to such agressive snowfall forecasts should the band move over Norman. All of the model members of the SREF were forecasting the band to move overhead before sunrise and the final accumulations of  Snow Water Equivalent (SWE) ranged from 0.3 to 0.97".  These totals were in range to deliver us significant snowfall.  The highlighted ARW KF SREF member gave us ~0.5".
Figure 5  Like figure 1 except for QPF.  The highlighted SREF member is the ARW KF version of the WRF.  The bar plot at the bottom represent hourly accumulations.

But the snow accumulation is incredibly dependent on the forecasted density of the snowfall.  No model explicitly predicts snow density and so we're dependent on empirical relationships.  The technique used to come up with the snowfall forecasts in the figure 1 assumes that the snow density decreases as the surface temperature decreases.  See below the relationship between both parameters and you see what I mean.  This shows the snow ratio forecast exceeding 25:1 after 09 UTC, the highest values of all the techniques I present (see figure 6).  Basing the snow ratio from the surface temperature is often not a reasonable strategy since snow flakes, and their density, is dependent on the temperature and humidity where they form.  However if surface temperature approaches freezing then the snow pack may morph into a higher density.  This case is not a candidate for warm surface temperatures.

Figure 6  Time trace for a SREF member 21 UTC 08 Feb 2011 run with a snowfall near the average of the distribution.  In red is the 2m surface temperature (F) and the anticipated snowfall ratio (depth/SWE) is represented by the blue line.  The values for the snow ratio (2m temp) are labeled in the left (right) axis.  The white curve represents total snow accumulation.  The vertical bars at the bottom represent hourly snowfall accumulation. 

Instead of using the 2m temperature, perhaps the maximum temperature in the vertical profile (MaxTemp) may provide a more realistic snow ratio.  The snow ratio is inversely proportional to the MaxTemp.  The thinking behind the MaxTemp technique is that snow flakes entering into the warmest layer could be subjected to riming in which cloud liquid drops freeze directly onto the flakes helping to reduce interstitial spaces between ice and thereby increasing snow density and decreasing the snow to liquid ratio.  If we assume that MaxTemp is saturated then it seems reasonable that riming is more likely if MaxTemp is warmer because cloud liquid water content would also be higher. For this storm, the MaxTemp was forecasted to drop as the cold air deepened and thus the forecasted snow ratios for each SREF member increased with time.  The same SREF member we used above in figure 1 shows a lower snow ratio using the MaxTemp technique and the subsequent forecasted snowfall came out to nearly one foot, less than the 15" using the surface temperature. Even though the snow ratio is lower, it was still considerably higher than the mean snow ratio for central Oklahoma.

Figure 7  Like figure 6 except the snow accumulation and snow ratios are from the MaxTemp in profile snow ratio technique.  The yellow contours are temperature plotted as a function of time and height.
The next snow ratio technique, called the Zone Omega, evaluates the relationship between the vertical motion and temperature profile in the vertical.   In a brief explanation, the highest snow ratios occur when the greatest amount of lift occurs with the dendrite growth zone (-12 to -18 deg C) relative to the lift that occurs at warmer and colder temperatures. Likewise the highest snow ratios would occur if the vertical distribution of vertical motion falls outside the dendrite growth zone.  It so happens that the dendrite growth zone is the temperature layer in which cold phase precipitation production is most efficient, and that dendrites are prime candidate snow crystals to allow for the largest air spaces once dendrites aggregate.  So if the ascending air is focused in this layer, the predominant form of snow would be big fluffy, low density dendritic flakes (high snow ratio).  Vertical motion concentrated at lower levels (warmer temps) would yield snow flakes dominated by more compact needles at -5 deg C resulting in a lower snow ratio.  Likewise if the strongest vertical motion were concentrated at higher levels (lower temps) than the dendrite growth zone, then the predominate snow crystal habit would also be more compact plate, or column-shaped crystals resulting in a higher ratio. There is lots more discussion about this technique available at this address:  In addition, a Cobb and Waldstreicher (2005) is a good reference on this technique.

Considering the same SREF ARW WRF member as before, we find that the overall snowfall forecast decreased down to 9" in figure 8 when applying the Zone omega technique.  The snow ratio, in blue, was quite volatile as the level of peak ascent fell in and out of the dendrite growth zone (yellow contours).  Note that early on, the peak vertical motion was quite low resulting in a low snow ratio and then there was a relatively narrow window where the majority of ascent centered on the dendrite growth zone and the snow ratio spiked to 30:1 at 12-13 UTC on the 9th.  The greatest snowfall rate is more a function of the Zone Omega technique's huge snow ratios than the actual SWE rate visualized in figure 5. 

Figure 8  Similar to figure 6 except the Zone Omega technique is being used to calculate snow  fall.  In addition, instead of temperature, the contributing factors in the this technique include the vertical motion (red contours), and the dendrite growth zone (purple and yellow contours).  The yellow contours indicate when the dendrite growth zone is saturated. 

Just after the snow event ended around noon, I took a core sample of the snow using the standard 10" deep clearview rain gauge that is the standard for the COCORAHS observing network and melted it to get 0.37" of SWE.  Another similar gauge left open in the snow storm resulted in 0.41" of SWE.  Our SWE was below the featured SREF member (figures 5-8) but it was higher than the member with the minimum QPF.  So in short, our SWE was anticipated as a possibility according to the 21 UTC SREF model run.

Given a snow depth of only 2.7", my snow ratio was a paltry 6.6:1.  This value was well below even the most dense snow ratio technique applied above.  My snow ratio value was far below climatology as determined by Baxter et al. (2005) while the median value is near the median climatological value.  But all these values were well below the forecasted values by all SREF members, especially for those snow ratio techniques using temperature.  But even the Zone Omega technique overestimated the snow ratios during the forecasted maximum snowfall rates centered around 12 UTC.  But, earlier in the forecasted snowfall, the Zone Omega technique forecasted snow ratios < 10:1 when the maximum ascent didn't reach the dendrite production layer.

The measurements I mentioned so far represent the sum total of what happened in the storm.  But there's more complexity to the snow crystal types that yielded a broader variety of snow ratios.  I took a picture of our snow core balancing on the top of a ruler (official NWS ruler) and it showed some interesting changes in crystal types (fig. 9).  For instance, the lower third of the core consisted of tightly packed small crystals that appeared to be small graupel.  Above that layer, the middle third appeared to be small aggregates of small dendrites, still appearing quite dense.  Luckily, I measured the depth of these two layers before the third one fell in the late morning and got 2.2" of snow depth with 0.37" of SWE from the gauge and 0.31" from a core sample.  Just taking the 0.37" from the gauge, I got a snow ratio of only 5.9:1.  This layer of snow was dense, acting almost like machine-made snow but it was definitely not wet.  During the late morning, a final round of snow fell in the form of some of the biggest dendrites I've seen (see fig 10).  They were bundled up in large aggregates.  About 0.5" of snow accumulated with this last round and I got about .03 to .04" of SWE.  This ratio was a considerably larger 16:1, and quite expected for the flake type I saw. 

Figure 9  A picture of a snow core sample taken at 18 UTC 09 Feb 2011 showing a bottom layer of graupel, a middle layer of small dendrites and an upper layer of large dendrites.

Figure 10  A closeup picture of the upper layer of large dendrites that fell in the late morning of 09 Feb 2011 in east Norman.  Photo courtesy of Daphne LaDue.
Of all the snow ratio techniques that were used in this SREF model output, only the Zone Omega technique forecasted a similar broad range of values to what was observed.  Now, in the case of the Zone Omega technique, the forecast snow ratios were generally too high when the SWE rates were at their highest.  But at the start of the forecasted precipitation, the technique did forecast snow ratios less than 10:1 because the maximum ascent was expected to be centered well below the dendrite production zone.  Perhaps the technique represented some semblance of reality in central Oklahoma until the late morning when most of the snow ended. The morning sounding (fig. 10) from Norman during the first phase of the snow appears to support this idea since the cloud top may have barely risen into the heart of the dendrite production zone above 3 km MSL.   However the radar data showed a more complex picture.  The snow arrived in an almost convective band with reflectivities up to 30 dBZ at >5 km ARL around 1030 UTC.  This deep precipitation didn't last long so that by the time the sounding was launched at around 1115 UTC, the depth at maximum reflectivities fell to less than 3km ARL.   For most of the event, the observed snow production layer was quite shallow as observed by the KTLX radar.  Toward 16 UTC, the cooling aloft brought the dendrite production zone lower to phase with the layer of maximum ascent and as a result our last round of snow fell as low density dendrite aggregates.  The cold temperatures and weak ascent below this layer may have limited riming and additional higher density snow flake production.

figure 10.  A sounding display for Norman taken 09 Feb 2011, 12 UTC.

All of the snow ratio techniques that I discussed do little to consider the effects of solar radiation, temperature and wind upon the density of the snow pack.  I decided to measure the snow ratio after the end of the snow events, the first measurement coming at 13 UTC and the final one at 18 UTC after the large dendrites finished falling.  Temperatures near freezing could accelerate crystalline metamorphasis into denser forms and the snowpack density could increase.  There was some wind which could've broken the crystals upon landing and increased the density.  Roebber et al. (2003) described in detail these time dependent processes that alter the density of freshly fallen snow.  However, the temperatures for this event were less than 15 deg F and so I was not concerned about melting.  In addition, the snow core pictures didn't support the contention that the wind was strong enough to break a majority of crystals.   There was some natural settling to consider that may bring down the snow ratio forecasts a bit. BUFKIT attempts to account for settling by applying an exponential decay function to the forecast snow depth.  The effects of this function can be seen in figures 6-8.  Most of my measurement times were near the forecasted peak snowdepth and so this effect wasn't very significant.  

The Zone Omega technique may have won out in this case but I wouldn't vouche for its continued relative success for every event.  This technique doesn't account for errors in the vertical motion field, or other processes that include riming, and changes to snowpack density due to settling, wind, and melting.   In fact, for a well known New York City snowstorm on 26 January 2011 where 19" of snow fell in Central Park, the Zone Omega technique forecasted snow ratios that were far too high than observed.  In that case, relatively maximum elevated temperatures were closer to freezing and that layer featured a very strong flow ascending over the frontal surface ahead of strong low-level cyclogenesis.  In that case, the max temp in profile technique beat all others perhaps because that technique applies well when significant riming, and warm ice crystal production occurs in the face of strong saturated ascent at relatively warm temperatures.

Bottom line:

Our observed SWE was actually contained within the envelope of possible QPF based on the 21 UTC SREF.

The surface temperature and MaxTemp snow ratio techniques bombed terribly because the temperatures were cold.  Clearly these techniques failed to represent the mechanisms influencing the density of falling snow.  Dense snow can occur at very cold temperatures, surface or aloft.

The ZoneOmega technique performed the best of the three techniques but still far overestimated the snowfall.  Given the small snow ratios observed, and the compact crystal nature seen in the snow core, I suspect that much of the precipitation was forming below the dendrite production zone perhaps because the vertical motion field was too shallow.   Only when the temperatures cooled did the shallow vertical motion extend into the dendrite production zone.  Still, this technique did better than the others.  Don't expect this to be true all the time, however.


Baxter, A. A., C. E. Graves, J. T. Moore, 2005: A Climatology of Snow-to-Liquid Ratio for the Contiguous United States. Wea. Forecasting, 20, 729–744.  

Cobb, D. K., and J. Waldstreicher, 2005:  A simple physically-based snowfall algorithm.  Preprints, 21st Conf. on Weather Analysis and Forecasting, Washington D.C., American Meteorological Society

Roebber, P. J., S. L. Bruening, D. M. Schultz, J. V. Cortinas, 2003: Improving Snowfall Forecasting by Diagnosing Snow Density. Wea. Forecasting, 18, 264–287. 

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