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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.
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Sophie Splawinski 1 Honors BSc. Atmospheric and Oceanic Sciences MSc. Atmospheric Sciences Prof. John R. Gyakum1 Dr. Eyad H. Atallah1 Benjamin Borgo2 1McGill University, Montreal, Quebec2Washington University, St-Louis, Missouri The Prediction of Onset and Duration of Freezing Rain in the Saint-Lawrence River Valley
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 Freezing Rain Frequency in North America Figure i. Frequency of freezing rain over an 10yr period (1979-1990). Courtesy of the Department of Meteorology at Penn State University 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 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). Phase Change Phase Change SN P(SLRV) Onset RA PN(SLRV) Onset RA UP(NS) Onset Phase Change FZDZ UP(EW) Onset Phase Change
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 • 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 • good fit: (p-value less than 0.05 for both 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.
The best approach:Not enforcing a temperature difference... • 2D elliptical Gaussian model • Data is very close to normally distributed. • Steps: • normalize all known null observations • gives mean upper and lower surface temperatures and no FZRA • Fit 2D elliptical Gaussian to the binned, null data • model: • optimal values: α= 0.103255, β= 0, ϒ = 0.049962 • 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 • 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 etal. (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 Partitioning technique of geostrophic relative vorticity at 850hPa PN (SLRV): Maxima of cyclonic vorticity located N of the SLRV. P (SLRV): Maxima of cyclonic vorticity located within the SLRV. UP (EW): Straight-line east-west oriented geostrophic flow with a north-south couplet of high and low pressure. UP (NS): Straight-line north-south oriented geostrophic flow with small, disorganized vorticity maxima.
pressure gradient vs. duration Pressure Gradients for all four sub-categories at YQB Gradient: aligned along the SLRV- 50km SW, 50km NE SN P (SLRV) (18h) RA P (NSLRV) (15h) FZDZ UP (EW) (24h) RA UP (NS) (15h)
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.
CPOZR: YQB PG at phase change and CPOZR 50% 50% CPOZR: YUL • 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?