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A Simple Physically Based Snowfall Algorithm Daniel K. Cobb Jr. Science Operations Officer WFO – Caribou, ME

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

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Page 1: A Simple Physically Based Snowfall Algorithm

A Simple Physically Based Snowfall

AlgorithmDaniel K. Cobb Jr.

Science Operations Officer

WFO – Caribou, ME

Page 2: A Simple Physically Based Snowfall Algorithm

Introduction

I. Motivation and GoalsII. Description of AlgorithmIII. Example CaseIV. SummaryV. Future WorkVI. ReferencesVII. Questions

Page 3: A Simple Physically Based Snowfall Algorithm

Motivation & Goals

• Improve on 10:1 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

HISTORYHISTORY

• 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 (-12°C and -18°C)

• 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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AlgorithmFOUR STEP PROCESS

1. Layer snow ratios are calculated for all available NWP levels based on temperature.

2. The vertical motion of each layer is scaled based on the relative humidity of the layer.

3. A column total vertical motion is calculated as the sum of the scaled layer vertical motion.

4. The layer snow ratios from step one are weighted by the percent of column vertical motion and summed to obtain a base snow ratio.

5. The base snow ratio is then multiplied by the QPF to obtain snowfall.

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Algorithm Example

T = -25C ω = -5 μbs-1

T = -15C ω = -10 μbs-1

T = -5C ω = -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 Snow Ratio as a Func tion of Sourc e Layer

Temperature

0.0

5.0

10.0

15.0

20.0

25.0

30.0

-30.0 -28.0 -26.0 -24.0 -22.0 -20.0 -18.0 -16.0 -14.0 -12.0 -10.0 -8.0 -6.0 -4.0 -2.0 0.0

Temperature ->

Sn

ow

Ra

io -

>

B ase Ratio

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Algorithm Example

SR = 8:1 %ω = -5/-20 μbs-1

SR = 24:1 %ω = -10/-20 μbs-1

SR = 9:1 %ω = -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 = 8:1 %ω = -5/-20 μbs-1

8.0 * 0.25 = 2.0

SR = 24:1 %ω = -10/-20 μbs-1

24.0 * 0.50 = 12.0

SR = 9:1 %ω = -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 = 16.3Or

~16:1

Page 14: A Simple Physically Based Snowfall Algorithm

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

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Example (2004Jan19)

• Localized heavy snowfall from pivoting inverted surface trough and eastward extending upper low.

• SOO’s 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 0.00727130 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

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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 100:1 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/micrope.html].

• Dube`, Ivan, 2003: From_mm_to_cm. COMET’s 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/hq/ssd/snowmicro/].

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Thank You

Question?