A Simple Physically Based Snowfall Algorithm

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A Simple Physically Based Snowfall Algorithm

• Daniel K. Cobb Jr.
• Science Operations Officer
• WFO Caribou, ME

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Introduction

1. Motivation and Goals
2. Description of Algorithm
3. Example Case
4. Summary
5. Future Work
6. References
7. Questions

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Motivation Goals

• Improve on 101 snow ratio assumption
• Incorporate aerial and temporal variation of snow
  ratio over a storm.

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Motivation Goals

• Develop a Snow Amount SmartTool for GFE
• Physically based population of snowfall from QPF
• Good base tool in terms of collaboration
• Develop complimentary snow amount/ratio code for
  use in Bufkit
• Excellent Interpretation/interrogation tool for
  forecaster

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Motivation Goals

• HISTORY
• Initial interest began in 2000.
• Idea further inspired by
• Top-Down microphysics of Baumgardt
• Crosshair approach of Waldstreicher
• Canadian snow ratio decision tree algorithm by
  Dubè
• Snow density diagnostic of Roebber

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Algorithm

• SNOW CRYSTAL BASICS
• Crystal habit depends
• Primarily on temperature
• Secondarily on relative humidity
• Largest crystals (dendrites) form at temperatures
  between (-12C and -18C)
• Crystal growth rates are also the largest in this
  temperature range.

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Algorithm
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Algorithm

• To a first approximation, the amount of cloud
  mixing ratio formed in any layer will be related
  to its relative humidity and vertical motion.
• This provides a basis for inferring the amount of
  crystal habit any one layer will contribute.

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Algorithm

• FOUR STEP PROCESS
• Layer snow ratios are calculated for all
  available NWP levels based on temperature.
• The vertical motion of each layer is scaled based
  on the relative humidity of the layer.
• A column total vertical motion is calculated as
  the sum of the scaled layer vertical motion.
• The layer snow ratios from step one are weighted
  by the percent of column vertical motion and
  summed to obtain a base snow ratio.
• The base snow ratio is then multiplied by the QPF
  to obtain snowfall.

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Algorithm Example
T -25C ? -5 µbs-1
T -15C ? -10 µbs-1
T -5C ? -5 µbs-1
Consider a 3 layer cloud with the following layer
average temperatures and vertical motion First
map temperatures to a snow ratio
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Algorithm Example
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Algorithm Example
SR 81 ? -5/-20 µbs-1
SR 241 ? -10/-20 µbs-1
SR 91 ? -5/-20 µbs-1
Layer temperature has now been mapped to snow
ratio (SR) The percent layer contribution to
vertical motion is now being calculated.
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Algorithm Example
SR 81 ? -5/-20 µbs-1 8.0 0.25 2.0
SR 241 ? -10/-20 µbs-1 24.0 0.50 12.0
SR 91 ? -5/-20 µbs-1 9.0 0.25 2.25
The weighted layer snow ratios are summed up over
the cloud yielding the base snow ratio. The snow
ratio would then be 2.0 12.0 2.3
16.3 Or 161
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Algorithm Example
The snowfall is obtained by multiplying the snow
ratio by the QPF. A QPF of 1.50 and the
calculated snow ratio of 161 would yield 1.50
16 24 inches
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Example (2004Jan19)

• Localized heavy snowfall from pivoting inverted
  surface trough and eastward extending upper low.
• SOOs neighborhood was ground zero with 21 inches
  of rather fluffy snow!
• Maximum snowfall rates approaching 3 inches per
  hour occurred at about 15Z on Jan19th.

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CarSnowAmt SmartTool

• Collaborators
• Dave Novak (ERH, SSD)
• Jeff Waldstreicher (ERH, SSD)
• Tom Lebvre (FSL)
• Test version now available from STR
• Currently useable with Eta80, Eta40, and WSEta.
  (GFS80 coming in OB4)

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Snow Amount Bufkit

• Planned incorporation into Bufkit
• Currently exists as Perl program which uses
  Bufkit files to perform calculations
• Compliments GFE SmarTool by allowing forcaster to
  critique the answer.
• Additional precipitation type logic currently
  being developed.

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Bufkit Example 2004Jan19
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StnID Date/hour FcstHR QPF SfcT
SnR Snow CumSnw CumQPF

727130 040118/1800 0 0.000 -7.8
0.0 0.0 0.0 0.00 727130 040118/1900
1 0.004 -6.9 20.4 0.1 0.1
0.00 727130 040118/2000 2 0.016
-7.0 19.5 0.3 0.4 0.02 727130
040118/2100 3 0.024 -7.0 19.9
0.5 0.9 0.04 727130 040118/2200 4
0.024 -7.2 17.1 0.4 1.3 0.07 727130
040118/2300 5 0.024 -6.8 20.0
0.5 1.7 0.09 727130 040119/0000 6
0.020 -6.5 16.8 0.3 2.1 0.11 727130
040119/0100 7 0.020 -6.1 15.7
0.3 2.4 0.13 727130 040119/0200 8
0.020 -5.8 15.4 0.3 2.7 0.15 727130
040119/0300 9 0.028 -5.8 15.1
0.4 3.1 0.18 727130 040119/0400 10
0.035 -5.9 14.8 0.5 3.6 0.21 727130
040119/0500 11 0.039 -5.8 15.0
0.6 4.2 0.25 727130 040119/0600 12
0.043 -5.9 14.8 0.6 4.8 0.30 727130
040119/0700 13 0.047 -5.9 14.7
0.7 5.5 0.34 727130 040119/0800 14
0.047 -6.0 14.9 0.7 6.2 0.39 727130
040119/0900 15 0.047 -6.0 15.2
0.7 7.0 0.44 727130 040119/1000 16
0.043 -6.2 15.2 0.7 7.6 0.48 727130
040119/1100 17 0.039 -6.2 14.3
0.6 8.2 0.52 727130 040119/1200 18
0.039 -6.2 14.0 0.6 8.7 0.56 727130
040119/1300 19 0.043 -6.0 14.4
0.6 9.3 0.60 727130 040119/1400 20
0.047 -5.4 14.9 0.7 10.1 0.65 727130
040119/1500 21 0.051 -4.9 15.0
0.8 10.8 0.70 727130 040119/1600 22
0.055 -4.6 15.2 0.8 11.7 0.76 727130
040119/1700 23 0.051 -4.1 15.8
0.8 12.5 0.81 727130 040119/1800 24
0.043 -3.7 15.7 0.7 13.1 0.85 727130
040119/1900 25 0.039 -3.5 16.1
0.6 13.8 0.89 727130 040119/2000 26
0.035 -3.6 16.1 0.6 14.3 0.93 727130
040119/2100 27 0.031 -4.1 16.6
0.5 14.9 0.96 727130 040119/2200 28
0.028 -4.6 16.0 0.4 15.3 0.98 727130
040119/2300 29 0.024 -4.8 15.4
0.4 15.7 1.01 727130 040120/0000 30
0.020 -5.3 14.9 0.3 16.0 1.03
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Verification (PQI) 2004Jan19
Date Time Snow Equiv Ratio
01/18 18Z 24Z 2.3 0.15 15.3
01/19 00Z - 12Z 9.8 0.61 16.1
01/19 12Z 18Z 8.6 0.42 20.5
01/19 18Z 24Z 0.8 0.08 10.0
Storm Total 21.5 1.26 17.1
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Eta Forecast 01/17 12Z
Location Snow Equiv Ratio
Caribou 9.7 0.58 16.7
Houlton 13.8 0.84 16.4
Millinocket 12.6 0.82 15.4
Bangor 8.2 0.67 12.2
Eastport 9.9 0.83 12.0
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Summary

• Initial results A weighted average approach to
  snow-ratios works well.
• Such an approach is computer calculation
  friendly.
• Predicted ratios are very similar to those found
  using Dubè decision tree.
• Decision trees are people friendly.
• Applying snow-ratio diagnostic techniques
  improves forecast location of snowfall amounts as
  well as snowfall axes.

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Future Work

• Snow ratios up to 1001 have been observed
• This is often the result of aggregates of
  spatially large dendrites. The aggregate being
  less dense than its constituent crystals.
• Comprehensive snow study at WFO-CAR
• Two sonic depth sensors
• Measurements planned at 1, 3, and 6 hours.
• ASOS LEDWI snowfall algorithm tests

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References

• Baumgardt, Dan, 1999 WintertimeCloud
  Microphysics Review. NWS Central Region,
  Available online at http//www.crh.noaa.gov/arx/m
  icrope.html.
• Dube, Ivan, 2003 From_mm_to_cm. COMETs
  Northern Latitude Meteorology Webpage,
  http//meted.ucar.edu/norlat/snowdensity/from_mm_t
  o_cm.pdf.
• Roebber, P. J., S. L. Bruening, D. M. Schultz,
  and J. V. Cortinas Jr., 2002 Improving Snowfall
  Forecasting by Diagnosing Snow Density. Wea.
  Forecasting, 18, 264-287.
• Waldstreicher, J.S., 2001 The Importance of Snow
  Microphysics for Large Snowfalls, Preprints, 3rd
  Northeast Operational Workshop NOAA/NWS Albany,
  NY, Available online at http//www.erh.noaa.gov/e
  r/hq/ssd/snowmicro/.

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Thank YouQuestion?