THE PREDICTION OF ONSET AND DURATION OF FREEZING RAIN IN THE SAINT-LAWRENCE RIVER VALLEY Sophie Splawinski 1 Honors BSc. Atmospheric and Oceanic Sciences MSc. Atmospheric Sciences Prof. John R. Gyakum 1 Dr. Eyad H. Atallah 1 Benjamin Borgo 2 1 McGill University, Montreal, Quebec 2 Washington 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 ( ). 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 (courtesy of Alissa Razy)

DATA (CYUL & CYQB) 30-year period ( ) 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: severe FZRA events (n=46 CYUL, n=47 CYQB) 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: degrees CYQB: 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) OnsetPhase ChangeFZDZ UP(EW) OnsetPhase 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

PROBABILITY OF FREEZING RAIN (POZR): APPROACH We define the following variables: And calculate the following probabilities: N f = # of days with ZR N = # of days without ZR n d,f = # of days with ZR and a given temperature difference d n d = # of days without ZR and a given temperature difference d P(F) = Probability of ZR P(T d ) = Probability of a given temperature difference d P(T d |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 R 2 = 0.9 model pictured according to the formula: Best fit when: A = B = 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: p 1, p 2 = 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 T sfc < T 850 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

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 MODELS HOW 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. sfc850hPaexponentiallogisticalgebraic logistic algebraic HS logistic -5-24%98%7%0% %97%5%0% % 100%70%0% 13%97% 5%40% %76%0.1%0% %80%0.2%0% -811%99% 30%19% %99% 50%0% -417%99%15%81% -3411%99%30%17% %98%9%19% -6111%99%30%13% %80%0.2%0% %92%1%0% 045%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= , β= 0, ϒ = 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= , a= , b= , c= , B= model fits data extremely well (sum of squares residual is 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 sfc850hPaalgebrai c HS logistic 2D Gaussia n 2D gaussian with step -5-20% 30%0% % % 1 40% 52% 5-20% % % -4181% 93% % 70% % 80% % 72% % % 04 31% 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 s -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. DURATION PRESSURE GRADIENTS FOR ALL FOUR SUB-CATEGORIES AT YQB SN P (SLRV) (18h) RA P (NSLRV) (15h) RA UP (NS) (15h) 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: μ 1 - μ 2 = 0 alternative hypothesis: μ 1 > μ 2 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: μ 1 - μ 2 = 0 alternative hypothesis: μ 1 ≠ μ 2 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%1.2590% 20%0.2980% 30%0.1070% 40% % 50%50% 60% % 70% % 80% % 90% % % events change phase pressure gradient (mb) % events that continue 10%2.5890% 20%1.5080% 30%0.8870% 40%0.6760% 50%0.0050% 60% % 70% % 80% % 90%-3.310% CPOZR: YQB CPOZR: YUL 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?