# 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. Introduction. Motivation and Goals Description of Algorithm Example Case Summary Future Work References Questions. Motivation & Goals. Improve on 10:1 snow ratio assumption - PowerPoint PPT Presentation

### Text of A Simple Physically Based Snowfall Algorithm

• A Simple Physically Based Snowfall AlgorithmDaniel K. Cobb Jr.Science Operations OfficerWFO Caribou, ME

• IntroductionMotivation and GoalsDescription of AlgorithmExample CaseSummaryFuture WorkReferencesQuestions

• Motivation & Goals

Improve on 10:1 snow ratio assumption

Incorporate aerial and temporal variation of snow ratio over a storm.

• Motivation & GoalsDevelop a Snow Amount SmartTool for GFEPhysically based population of snowfall from QPFGood base tool in terms of collaboration

Develop complimentary snow amount/ratio code for use in BufkitExcellent Interpretation/interrogation tool for forecaster

• Motivation & GoalsHISTORY

Initial interest began in 2000.Idea further inspired by Top-Down microphysics of BaumgardtCrosshair approach of WaldstreicherCanadian snow ratio decision tree algorithm by DubSnow density diagnostic of Roebber

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

• Algorithm

• 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.

• AlgorithmFOUR 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.

• Algorithm ExampleConsider a 3 layer cloud with the following layer average temperatures and vertical motion:

First map temperatures to a snow ratio:

• Algorithm Example

Chart1

7

6.6608514301

6.9573622881

8.5251920021

12

17.4536350439

22.7027032329

25

22.5442757376

17.3181006748

12.25

9.5633606992

8.6610169492

8.2406647246

7

4.0306541314

Base Ratio

Temperature ->

Snow Raio ->

Snow Ratio as a Function of Source Layer Temperature

Sheet1

Aproximate snow to water ratio table assuming 10 (cm/sec )

H85-H100 ( m )H70-H85 ( m )H50-H70 ( m )M-Temp ( C )Base Ratio

115613812392-30.07.0-30.0000

116513922412-28.06.7-28.0000

117514032432-26.07.0-26.0000

118414152452-24.08.5-24.0000

119414262471-22.012.0-22.0000

120314372491-20.017.5-20.0000

121314492511-18.022.7-18.0000

122214602530-16.025.0-16.0000

123214712550-14.022.5-14.0000

124114832570-12.017.3-12.0000

125114942589-10.012.3-10.0000

126015062609-8.09.6-8.0000

127015172629-6.08.7-6.0000

127915282648-4.08.2-4.0000

128915402668-2.07.0-2.0000

1298155126880.04.00.0000

1308156227082.00.02.0000

Multiplier table for actual vertical motion

V (cm/sec)Percent Ratio

0.000.00

5.000.91

10.001.00

15.001.10

20.001.20

25.001.31

30.001.44

35.001.58

40.001.73

45.001.89

50.002.07

Multiplier for SFC Wind

U (kts)Percent Ratio

0.001.00

5.000.97

10.000.94

15.000.90

20.000.88

25.000.85

30.000.82

35.000.79

40.000.77

45.000.74

50.000.72

Multiplier for SFC Temperatures

T (F)

301.00

310.98

320.95

330.50

340.15

350.00

j

0-30.007.00-0.22250.00000.0132

1-22.0012.002.32010.3178-0.0572

2-16.0025.00-0.0472-0.71240.0610

3-10.0012.25-2.00640.3858-0.0271

4-2.007.00-1.0425-0.26530.0221

52.000.000.0000

Steps 4 - 6:

istep 1: (h)Step 2: (alpha)(mu)(z)(l)

08.00000.00000.00001.0000

16.00004.62500.21430.165228.0000

26.0000-12.87500.2642-0.610522.7143

38.00004.40630.30290.305526.4151

44.0000-3.28130.1854-0.265321.5771

50.0000

Sheet1

Base Ratio

Temperature ->

Snow Raio ->

Snow Ratio as a Function of Source Layer Temperature

Sheet2

Sheet3

• Algorithm ExampleLayer temperature has now been mapped to snow ratio (SR)

The percent layer contribution to vertical motion is now being calculated.

• Algorithm ExampleThe 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 = 16.3Or~16:1

• 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 16:1 would yield:

1.50 * 16 = 24 inches

• 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.

• CarSnowAmt SmartTool

CollaboratorsDave Novak (ERH, SSD)Jeff Waldstreicher (ERH, SSD)Tom Lebvre (FSL)

Test version now available from STRCurrently useable with Eta80, Eta40, and WSEta. (GFS80 coming in OB4)

• Snow Amount BufkitPlanned incorporation into BufkitCurrently exists as Perl program which uses Bufkit files to perform calculationsCompliments GFE SmarTool by allowing forcaster to critique the answer.Additional precipitation type logic currently being developed.

• Bufkit Example 2004Jan19

• StnID Date/hour FcstHR QPF SfcT SnR Snow CumSnw CumQPF=========================================================================727130 040118/1800 0 0.000 -7.8 0.0 0.0 0.0 0.00727130 040118/1900 1 0.004 -6.9 20.4 0.1 0.1 0.00727130 040118/2000 2 0.016 -7.0 19.5 0.3 0.4 0.02727130 040118/2100 3 0.024 -7.0 19.9 0.5 0.9 0.04727130 040118/2200 4 0.024 -7.2 17.1 0.4 1.3 0.07727130 040118/2300 5 0.024 -6.8 20.0 0.5 1.7 0.09727130 040119/0000 6 0.020 -6.5 16.8 0.3 2.1 0.11727130 040119/0100 7 0.020 -6.1 15.7 0.3 2.4 0.13727130 040119/0200 8 0.020 -5.8 15.4 0.3 2.7 0.15727130 040119/0300 9 0.028 -5.8 15.1 0.4 3.1 0.18727130 040119/0400 10 0.035 -5.9 14.8 0.5 3.6 0.21727130 040119/0500 11 0.039 -5.8 15.0 0.6 4.2 0.25727130 040119/0600 12 0.043 -5.9 14.8 0.6 4.8 0.30727130 040119/0700 13 0.047 -5.9 14.7 0.7 5.5 0.34727130 040119/0800 14 0.047 -6.0 14.9 0.7 6.2 0.39727130 040119/0900 15 0.047 -6.0 15.2 0.7 7.0 0.44727130 040119/1000 16 0.043 -6.2 15.2 0.7 7.6 0.48727130 040119/1100 17 0.039 -6.2 14.3 0.6 8.2 0.52727130 040119/1200 18 0.039 -6.2 14.0 0.6 8.7 0.56727130 040119/1300 19 0.043 -6.0 14.4 0.6 9.3 0.60727130 040119/1400 20 0.047 -5.4 14.9 0.7 10.1 0.65727130 040119/1500 21 0.051 -4.9 15.0 0.8 10.8 0.70727130 040119/1600 22 0.055 -4.6 15.2 0.8 11.7 0.76727130 040119/1700 23 0.051 -4.1 15.8 0.8 12.5 0.81727130 040119/1800 24 0.043 -3.7 15.7 0.7 13.1 0.85727130 040119/1900 25 0.039 -3.5 16.1 0.6 13.8 0.89727130 040119/2000 26 0.035 -3.6 16.1 0.6 14.3 0.93727130 040119/2100 27 0.031 -4.1 16.6 0.5 14.9 0.96727130 040119/2200 28 0.028 -4.6 16.0 0.4 15.3 0.98727130 040119/2300 29 0.024 -4.8 15.4 0.4 15.7 1.01727130 040120/0000 30 0.020 -5.3 14.9 0.3 16.0 1.03

• Verification (PQI) 2004Jan19

• Eta Forecast 01/17 12Z

• 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 Dub decision tree.Decision trees are people friendly.

Applying snow-ratio diagnostic techniques improves forecast location of snowfall amounts as well as snowfall axes.

• Future WorkSnow ratios up to 100:1 have been observedThis is often the result of aggregates of spatially large dendrites. The aggregate being less dense than its constituent crystals.Comprehensive snow study at WFO-CARTwo sonic depth sensorsMeasurements planned at 1, 3, and 6 hours.ASOS LEDWI snowfall algorithm tests

• ReferencesBaumgardt, Dan, 1999: WintertimeCloud Microphysics Review. NWS Central Region, [Available online at http://www.crh.noaa.gov/arx/micrope.html].

Dube`, Ivan, 2003: From_mm_to_cm. COMETs Northern Latitude Meteorology Webpage, http://meted.ucar.edu/norlat/snowdensity/from_mm_to_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/er

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