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
