On Environment and Climate Change Canada (ECCC) Radar Snowfall

Rate Estimates

Peter A. Taylor, Diar Hassan and George A. Isaac

CRESS, York University, Toronto, Canada, Wood PLC, Ottawa, Ontario, Weather Impacts Consulting Inc, Barrie, Ontario

Diar Hassan’s PhD thesis included development of snowfall rate relationships with radar reflectivity. These suggested that the ECCC radar displays of snowfall rates, based on Sekhon-Srivastava (1970), were too low – needing to be doubled, but it may be that ECCC were using a modified dBZ, different from the dBZe that we had assumed

The puzzle was why it was so wrong. There is a lot of variability in snow, ground level measurements are a problem etc. etc. but estimations that are only 50% of what is observed is a problem. NWS and OPERA (European radar) avoid the problem by just showing Ze on their public sites.

13 March 2020

Power law fit from Hassan et al (2017) with data from Oakville, YYZ and Mount Pearl (NL)

S&S (1970) with Ze, SWE R = 0.0338 Ze0.4525 ----------

Huang et al (2010) SWE R = 0.0345 Ze0.6329 -----------

S&S Ze

The Background: From Fabry, 2015. Radar Meteorology, Cambridge University Press

King radar, wavelength λ = 5 cm, |K|2

Dish size, Pulse length, transmittance

If the target is ice and |Kw|2Ze = |Ki|2Z then Ze =

(0.176/0.93) Z. This would give Z = Ze + 7.2 dB, but

ECCC, and others, actually use + 6.5 dB using melted

ice diameters in the Z definition, since

10log10[(ρi/ρw)6/3]=20log10[0.92] = -0.72.

Z = ∫ N(D)D6dD in mm6m-3.

N(D) is the drop size distribution,

and in decibels

dBZ = 10 log10(Z/1.0 mm6m-3)

0.176 (ρs/ρi)2 for snow in Marshall and Gunn (1952). Fabry

argues that snowflakes reflect slightly more radar energy than ice particles of the same mass.

ECCC measure values of |K|2 Z and could estimate Z (mm6m-3), and Z = 10 log10Z, in dB, from the radar return signals (where |K|2 is the dielectric constant of the hydrometeors). In practice ECCC radars, and other weather services, compute Ze with a water dielectric constant. There is also an adjustment due to ice/water density differences and, in effect, the reflectivity (Z) of “melted diameter” ice spheres is Ze + 6.5 dB.

How about snowfall rate? From Fabry we have, for rain, with wr(D) as the terminal velocity or fall speed.

This would also apply for snow IF we used D as the melted drop diameter and knew N(D) and wr(D) for snowflakes that would allow us to find a Z-R relationship.

From various snowflake measurements, including those by Gunn and Marshall (1958), Sekhon and Srivastava (1970) obtained the relationship Z = 1780R2.21 where R is Snow Water Equivalent precipitation rate and Z is based on melted drop diameters. This is based on power laws fitted to give size distribution and fall speed relationships. Note that Z is NOT Ze but it is based on melted snowflake diameters, D. Z would have to be obtained from the radar backscatter data and a knowledge of an appropriate dielectric constant for snowflakes.

Inverting the S-S relationship gives a snowfall rate, in SWE, R = 0.0335 Z0.4525. This is the relationship used by ECCC with, I now discover!, Ze + 6.5 as an appropriate Z.

If we want to use the S-S relationship as intended, we need to determine an appropriate dielectric constant, |K|2 for snowflakes. A simple way is to accept Smith’s (1984) estimate that “the radar cross section of an irregular particle composed of a weak dielectric like ice is the same as that of a sphere of the same mass”. This follows from work by Marshall and Gunn (1952) and led Smith to his version of the S-S relationship,

Ze(in dBz) = 26 +22.1 log10R (Eqn 14 in Smith, 1984)

In terms of mm6m-3, Ze = 398 R2.21. This was apparently in use for snow in Finland until 2004 (Saltikoff et al, 2015). Inverting that then gives R(SWE) = 0.0666 Ze

0.4525 .

Note that 0.0666/0.0335 is close to 2 and explains the problem with the snowfall rates predicted by Hassan et al (2015) with the S-S relationship applied with Ze. I had done the same and then discovered (last week) it in Smith’s paper! (Dr. Paul L. Smith passed away on May 10, 2019 after a short illness. He enjoyed 86 years of hijinks, discovery and love. – from South Dakota School of Mines obituary) Was once a PDF at McGill.

Newfoundland had snow in January 2020 and in particular on Jan 17.

(35 cm in 6 hours (1200-1800 UTC at CYYT )

CYYT METARS

Jan 17, 0800 to 1200UTC, 5cm

Jan 17, 1200 to 1800UTC, 35cm

Jan 18, 1800 to 0000UTC, 19cm

Jan 18, 0000 to 0500UTC, 15cm

Jan 18, 0500 to 1000UTc, 1cm

Note that dBZ to cm/hr assumes SWE R = 0.0338 Ze

0.4525

And snow density relative to water is 0.1.

The bands were travelling S to N. Holyrood radar seems to have blockage to the S and strong ground clutter to the N.

Reading off the historical radar imagery close to St John’s airport. My CYYT estimate from 10 min and 30 min Holyrood radar imageryJan 17, 12Z-18Z has max 4 cm/hr but mostly below 2 cm/hr. Best estimate of total accumulation based on ECCC radar is 10 cm.

For Jan 17, 18Z - 00Z Jan 18Max 2 cm/hr, mostly 1 cm/hr. Total 6.5 cm in 6 hrs. METAR had 19 cm.

My Remote Sensing of the Atmosphere class have been set the same assignment – will see what they estimate.

dBZ to cm/hr problems.

Internally King radar use Ze and adjust S-S based on essentially the same analysis as used above, by FMI and from Smith. This is used for snowfall accumulation calculations and should be OK.

On the public web site the dBZ has had 6.5 added and the original S-S coefficients are applied. This should also be OK.

The problem is still that snowfall rates from the radar backscatter appear to be seriously low.

Public web site

Precip-ET - SNOW Precip-ET - RAIN

References

Fabry, F., 2015, Radar Meteorology, Principles and Practice, CUP, 256pp.

Gunn, K. L. S., and J. S. Marshall, 1958: The distribution with size of aggregate snowflakes. J. Meteor., 15, 452–461,

Hassan, D., Taylor, P.A. and Isaac, G.A., 2017, Snowfall rate estimation using C-band polarimetric radars, Meteorological Applications, 24, 142-156

Marshall, J.S. and Gunn, K.L.S., 1952, Measurement of snow parameters by radar, J Meteorology, 9, 322-327

Saltikoff, Elena, Philippe Lopez, Antti Taskinen and Seppo Pulkkinen, 2015, Comparison of quantitative snowfall estimates from weather radar, rain gauges and a numerical weather prediction model, BOREAL ENVIRONMENT RESEARCH 20: 667–678

Sekhon, R.S. and Srivastava, R.C. 1970. Snow size spectra and radar reflectivity. J. Atmos. Sci. 27: 299–307.

Smith, P.L. 1984. Equivalent radar reflectivity factors for snow and ice particles. Equivalent radar reflectivity factors for snow and ice particles. J. Appl. Meteorol. Climatol. 23: 1258–1260.