THE PREDICTION OF ONSET AND DURATION OF FREEZING RAIN IN THE

SAINT-LAWRENCE RIVER VALLEY

Sophie Splawinski 1

Honors BSc. Atmospheric and Oceanic SciencesMSc. Atmospheric Sciences

Prof. John R. Gyakum1 Dr. Eyad H. Atallah1

Benjamin Borgo2

1McGill University, Montreal, Quebec2Washington University, St-Louis, Missouri

INTRODUCTION

• Freezing rain (FZRA): hazardous meteorological phenomenon• high frequency in the Saint-Lawrence River Valley (SLRV)

• In the Quebec region:• An area where not much climatological research has been done

on FZRA• Splawinski et al. (2010, 2011)• Ressler et al. (2010)

• Start out point: Focus on Quebec City. • 2010: Atmospheric circulations and patterns associated with

FZRA• 2011: Role of Anticyclones• 2012: Putting it all together: across the SLRV, encompassing

major cities (CYUL and CYQB). • Goal: Providing meteorologists with tools to predict both the onset

and duration of FZRA.

OBJECTIVES

• Our goal: provide meteorologists with tools to predict both the onset and duration of FZRA.• From a general understanding of the vertical

structures conducive to FZRA:• Sub-zero shallow surface layer• Above-zero layer aloft

• From our 2011 work on anticyclones:• Role of surface cold air replenishment• It all comes down to pressure gradients

• Could we somehow utilize this knowledge to come up with a good forecasting tool?

FZRA AND THE SLRV

Annual bimodality of Winds at CYUL

Figure i. Frequency of freezing rain over an 10yr period (1979-1990). Courtesy of the Department of Meteorology at Penn State University

Freezing Rain Frequency in North America

Figure ii. Wind rose showing the climatological bimodal distribution of hourly observed surface winds at Montreal, Quebec (CYUL) from 1979-2002. (courtesy of Alissa Razy)

DATA(CYUL & CYQB)

• 30-year period (1979-2008)• Months: November-April• Severe FZRA events were determined using hourly

surface observations from Jean-Lesage Intl Airport (CYQB) and Pierre Elliotte Trudeau Intl Airport (CYUL)• Definition of severe event: FZRA lasting at least 6 h with at

most 4h of intermittent non-FZRA reports• 47 severe events at CYQB • 46 severe events at CYUL

• Analyses conducted using the North American Regional Reanalysis (NARR) dataset. • graphics created using GEMPAK• WRPlot used to create wind roses

STARTING WITH VERTICAL STRUCTURE:A METHODOLOGY FOR OUR STATISTICAL MODELS

• Goal: finding a method to predict the onset of FZRA• For each city, the data collection periods were identical:• 1979-2008 severe FZRA events (n=46 CYUL, n=47 CYQB)• 1979-2008 null events (n=478 CYUL, n=858 CYQB)• Null events defined as:

• At least 6h of precipitation, with at most 4h of intermittent non-precip reports

AND• At least 6h of northeasterly winds, with at most 4h of intermittent non-NE

wind reports

• Northeasterly winds defined following the orography of the SLRV:• CYUL: 20-70 degrees• CYQB: 40-90 degrees• Basis: pressure gradients are oriented along the SLRV and throughout

events predominantly from the NE.

PRESSURE GRADIENT EXAMPLE:CYQB: WIND ROSES

SN P(SLRV) Onset Phase Change RA PN(SLRV) Onset Phase Change

RA UP(NS) Onset Phase Change FZDZ UP(EW) Onset Phase Change

Wind roses comprised of all events within that subcategory. The rose points in the direction from which the wind is blowing, and colors depict associated wind speeds (m/s).

VERTICAL STRUCTURE CON’T

• At onset for severe FZRA events:• retrieved surface temperatures using Environment

Canada’s National Climate Archive (hourly temperatures).• retrieved warmest upper level temperature and pressure at

which it occurred using NARR.• note: NARR is three hourly, thus a temperature interpolation

was done using the nearest NARR hour available, the actual time of onset, and the hour following/preceding it.

• For null events: same approach only upper level temperatures were retrieved using the 850 hPa pressure level.

• Mean pressure level for FZRA events: 850hPa, standard dev: 38hPa

PROBABILITY OF FREEZING RAIN(POZR): AN INTRODUCTION

• Forecasting the ONSET of FZRA:• Robust (includes both FZRA and null events) 30 yr

climatological model comprised of all precipitation events that had both prolonged northeasterly wind and precipitation.• We will start with the simplest approach then go through

each predictor and what is needed to provide the best predictions possible.

• Forecasts would therefore be built by analyzing the probability of FZRA given both surface and upper level (850hPa) temperatures in both freezing rain and null events. • Basis: probability of FZRA at different surface and upper level

temperatures—putting the two together.

• This method could be extrapolated to similar regions of orographic influence (ie: pressure driven channeling)

PROBABILITY OF FREEZING RAIN(POZR): APPROACH

• Data was first binned according to 1 degree (°C) increments in temperature difference between the surface and 850hPa• Two separate distributions (days with/without FZRA)

FZRA days non-FZRA days

0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 11-12 12-13 13-14 14-15 15-16

PROBABILITY OF FREEZING RAIN(POZR): APPROACH

• We define the following variables:

And calculate the following probabilities:

Nf = # of days with ZR

N = # of days without ZR

nd,f = # of days with ZR and a given temperature difference

d

nd = # of days without ZR and a given temperature

difference d

P(F) = Probability of ZR

P(Td) = Probability of a given temperature difference d

P(Td|F) = Probability of a given temperature difference d

given

that ZR occurs

PROBABILITY OF FREEZING RAIN(POZR): RESULTS

• Using Bayes’ theorem, the probability of observing FZRA given a specific temperature difference, d, is:

• Plugging in our data set, we can compute the relevant probabilities and plot the results.• Two approaches: exponential and logistic regression• We will start with the most basic approach, then take a look

at how we could create a more realistic and reliable model.

PROBABILITY OF FREEZING RAIN(POZR): EXPONENTIAL

R2 = 0.9

model pictured according to the formula:

Best fit when:

A = 0.01942 B = 0.24827

• Disadvantage: tends to blow up at high temperature differences• We therefore then took a look at a logistic regression approach

PROBABILITY OF FREEZING RAIN(POZR): LOGISTIC REGRESSION

• good fit: (p-value less than 0.05 for both parameters)

• Advantage: doesn’t blow up at high temperature differences

• Disadvantage: may underestimate the probability of FZRA at high temperature differences (due to sample size)

• Equation fit in this case:

• p1, p2 = fit parameters

BEST RESULT FOR POZR:LOGISTIC REGRESSION WITH ALGEBRAIC

TEMPERATURE DIFFERENCE• Same analysis, but this time incorporating an

algebraic temperature difference.• Necessitating a temperature inversion to be present• Tsfc < T850 FZRA days

non-FZRA days

• x-axis: bins corresponding to temperature differences between 0 and 1, 1 and 2, etc...

• We see a very distinct separation of the two distributions, better than when we did not incorporate an algebraic temperature difference.

0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 11-12 12-13 13-14

LOGISTIC REGRESSION WITH ALGEBRAIC TEMPERATURE DIFFERENCE

• This model is fit according to the equation:

Where

LOGISTIC REGRESSION WITH DIRECTIONAL TEMPERATURE DIFFERENCE

• To ensure that probabilities would be computed as accurately as possible, we went a step further and incorporated Heaviside step functions• This would omit cases where temperature is decreasing with height

and the aloft temperature is less than some cutoff, C, which is the minimum temperature in the aloft measurement

• The best model for predicting the POZR:

• The conditional heaviside step function: enforces the condition that aloft temperatures must be greater than surface temperatures (or else P(FZRA)=0 )

• The second heaviside step function: enforces the condition that the aloft temperature must be either > 0 or no more than C degrees below zero. enforces temperatures < 0 at surface• Error can be adjusted to match errors being considered in each case.

TESTING THE MODELSHOW WELL DO THEY PERFORM?

• 15 random temperatures are chosen at both the surface and 850hPa, and then plugged into every model to see the forecast POZR.

sfc 850hPa exponential logistic algebraic logistic

algebraic HS logistic

-5 -2 4% 98% 7% 0%

-10 -8 3% 97% 5% 0%

-20 -9 30% 100% 70% 0%

-1 1 3% 97% 5% 40%

5 -2 0.3% 76% 0.1% 0%

7 1 0.4% 80% 0.2% 0%

-8 -1 11% 99% 30% 19%

-12 -3 18% 99% 50% 0%

-4 1 7% 99% 15% 81%

-3 4 11% 99% 30% 17%

-3 0.5 5% 98% 9% 19%

-6 1 11% 99% 30% 13%

-7 -13 0.4% 80% 0.2% 0%

-10 -12 1% 92% 1% 0%

0 4 5% 98% 10% 31%

THE BEST APPROACH:NOT ENFORCING A TEMPERATURE DIFFERENCE...

• 2D elliptical Gaussian model• Data is very close to normally distributed.• Steps:

1. normalize all known null observations• gives mean upper and lower surface temperatures and no FZRA

2. Fit 2D elliptical Gaussian to the binned, null data• model:

• optimal values: α= 0.103255, β= 0, ϒ = 0.049962

3. perform same binning and normalization for FZRA data, and fit a superposition of a candidate 2D elliptical Gaussian minus the weighted null model and optimize the Gaussian parameters and the null model weight.

2D ELLIPTICAL GAUSSIAN MODEL

• Freezing Rain Model:

• A=0.9999545, a=0.06333399, b=0.000024784, c=0.0716030999, B=0.00279933

• model fits data extremely well (sum of squares residual is 0.012799.

• Could improve the model by using smaller temperature bins, but would make data very sparse and improvement would only be incremental.

• Include Heaviside step functions as well, to impose conditions on surface and upper level temps

2D ELLIPTICAL GAUSSIAN MODEL: THE RESULTS

sfc 850hPa algebraic HS logistic

2D Gaussian

2D gaussian with step

-5 -2 0% 30% 0%

-10 -8 0% 0% 0%

-20 -9 0% 0% 0%

-1 1 40% 52% 52%

5 -2 0% 0% 0%

7 1 0% 0% 0%

-8 -1 19% 19% 19%

-12 -3 0% 0% 0%

-4 1 81% 93% 93%

-3 4 17% 70% 70%

-3 0.5 19% 80% 80%

-6 1 13% 72% 72%

-7 -13 0% 0% 0%

-10 -12 0% 0% 0%

0 4 31% 27% 27%

• does a much better job at giving high probabilities when temperatures are in a range normally associated with FZRA.

• if Heaviside functions are included: takes care of temperatures no in range.• again: could include

conditions that the meteorologist could manipulate.

• implementing this promising method could give the general public/emergency crews/airports a great “heads up” on when to potentially expect FZRA.

CONDITIONAL PROBABILITY OF FREEZING RAIN: (CPOZR)

• Stems primarily from work completed by Splawinski et al. (2011)• results from that study concluded that the location and

intensity of the downwind anticyclone played a large role in determining the duration of severe FZRA events

• the following method is therefore based entirely upon pressure gradient analysis

• “conditional”: FZRA precipitation has already started

• Extended to include CYUL so as to incorporate more of the SLRV.• again, this method can be implemented elsewhere, given

that the mechanisms for promoting a vertical profile conducive to FZRA are the same.

DEFINING FZRA CATEGORIES

• Events at YQB were first partitioned based on observed phase change over a 3hr period (6 categories)• Rain, Snow, FZDZ, Cloudy (3 types)• examples here: Rain, Snow, FZDZ

• Events were then partitioned into four sub-categories based on 850 hPa geostrophic relative vorticity• Threshold used: 24 x 10-5s-1

• Sub-categories had two main types: perturbed and unperturbed, each with two distinct axes of orientation

FZRA DURATION: AN EXAMPLE

P (SLRV): Maxima of cyclonic vorticity located within the SLRV.

PN (SLRV): Maxima of cyclonic vorticity located N of the SLRV.

UP (NS): Straight-line north-south oriented geostrophic flow with small, disorganized vorticity maxima.

UP (EW): Straight-line east-west oriented geostrophic flow with a north-south couplet of high and low pressure.

Partitioning technique of geostrophic relative vorticity at 850hPa

PRESSURE GRADIENT VS. DURATIONPRESSURE GRADIENTS FOR ALL FOUR SUB-CATEGORIES AT YQB

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

-4.5

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5START

END

SN P (SLRV) (18h)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

-4.5

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

START

END

RA P (NSLRV) (15h)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

-4.5

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

START

END

RA UP (NS) (15h)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

-4.5

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

START

END

FZDZ UP (EW) (24h)

Gradient: aligned along the SLRV- 50km SW, 50km NE

YUL VS YQB: CPOZR

• Wanted: diagnostic meteorological analysis at both cities• Can meteorologists use the simple PG calculation to

predict the duration of FZRA events?

• Research conducted by Gina Ressler (2012) of FZRA events at YUL• Same definition of severe events was used• 46 severe cases (vs. 47 at YQB)• PG calculation during severe event and during phase

change:• Weighted mean :

• test the significance of the obtained results

STUDENT T-TESTS Used to test means at YUL and YQB both during the severe event and at phase change.

• At each city:• testing whether the mean during the severe event vs mean

at phase change• null hyopthesis: μ1 - μ2 = 0

• alternative hypothesis: μ1 > μ2

• Test result: we can reject the null hypothesis at both 95%, 99% confidence

• Comparing both cities:• testing that means are the same at both cities during the

event and at phase change• null hyopthesis: μ1 - μ2 = 0

• alternative hypothesis: μ1 ≠ μ2

• Test result: fail to reject the null hypothesis at both 95%, 99% confidence

• Conclusion: YUL and YQB have statistically significant results, with similar pressure gradients both during the event and at phase change.

PG AT PHASE CHANGE AND CPOZR% events change phase

pressure gradient (mb)

% events that continue

10% 1.25 90%

20% 0.29 80%

30% 0.10 70%

40% -0.25 60%

50% -1.00 50%

60% -1.25 40%

70% -1.50 30%

80% -1.84 20%

90% -2.50 10%

% events change phase

pressure gradient (mb)

% events that continue

10% 2.58 90%

20% 1.50 80%

30% 0.88 70%

40% 0.67 60%

50% 0.00 50%

60% -0.40 40%

70% -1.06 30%

80% -1.65 20%

90% -3.3 10%

CPOZR: YQB

CPOZR: YUL

50% 50%

Findings:• Pressure gradients along the SLRV, at both YUL and YQB, provide an

excellent representation of the duration of severe freezing rain events.• Calculate pressure gradient along a 100km diameter (city located at

50km)• Utilize pressure gradient values as a means of forecasting the duration

of freezing rain.• Only valid once freezing rain has already begun• Quick and simple calculation could be obtained from forecast

models• Provides meteorologists with another forecasting tool to enhance

current methods of forcasting freezing rain

CONCLUSIONS

• Our results provide meteorologists with two models: • POZR: predicting the onset of FZRA using 2D elliptical Gaussian

model (preferentially with Heaviside step functions):

• CPOZR: predicting the duration of FZRA using pressure gradient calculations over a 100km diameter at the city in question, and then referring to the tables provided with given probabilities.

• Provides meteorologists with tools to further enhance their ability to forecast FZRA, and the public to prepare.

• Can be applied in other locations• CPOZR requires a similar orographic influence (pressure-driven

channeling), but POZR applicable in any FZRA situation

THANK YOU!

• Questions?