Added after class: completed calculation as PDF (numbers rounded) and as spreadsheet.
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With a sample size of 1356 after deleting missing data, the three equi-probable classes for Winnipeg February mean minimum temperature are defined by 33rd and 66th percentiles -24.4 and -15.6oC, i.e. the normal class for the minimum spans -24.4 to -15.6oC. The normal class for the maximum spans to -12.8 to -5oC. The corresponding normal classes for Edmonton's February (based on sample size 1272) are a considerably milder -16.7 to -8.6oC (normal minimum) and -7.2 to -1.8oC (normal maximum).
JDW's diagnosis: surface/850 hPa pattern, the Alberta lee trough; thermal ridge over Alberta, thermal trough over the east; somewhat humid, southwest upper flow. Partly cloudy (trend to increasing rather than decreasing cloudiness). Mild (up to about 10oC). Light S or SE wind. [As an aside: south of the Great Lakes and into S. Ontario, convective storms are expected.]
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Added after class: Matlab plot of energy balance components.
∂Td / ∂lnp = (273+Td)2 / (273 x 22.5)
which for Td=(-20, 0, 20)o evaluates to (10.4, 12.1, 14.0) K.
Interestingly, the corresponding Australian 120h global prog (accessed from Bureau of Meteorology, "BOM") is very different, showing only a weak remnant of this low pressure centre, some distance inland. However the Australian prog does place that storm on the coast at about 12Z Saturday 25 March, albeit as a much shallower centre... this BOM multipanel chart gives the path of the storm according to the Australian model. The Bureau of Meteorology issued this statement in regard to the system (from http://www.bom.gov.au/qld/forecasts/cyclone.shtml). The site weather-forecast.com gave this public forecast, with no sign of a tropical storm.
Please follow up on this discrepancy, by accessing the most recent available NWP guidance (GEM GDPS via Vizaweb and BOM Global) for NE Australia valid 12Z Monday 27 March. Very briefly record your interpretation on the weather forecast form.Added after class:
During 19-20-21 June 2013 severe flooding occurred in S. Alberta (here is the June 2013 weather record for Crowsnest Pass). Based on the CMC 700 hPa analysis analysis (12Z June 20th 2013) one might immediately guess a slow-moving upper low, directing a stream of moisture against the mountains, could have been the culprit (note: this is an extrapolation based only on this snapshot; of course other factors ought to be considered).
∇H • (uH q ) = ∂ (u q) / ∂x + ∂ (v q) / ∂ y
where q is the specific humidity. Note that where this quantity is negative, moisture is being suppied to the air column and represents a source for precipitation; note also that since q is dimensionless, the quantity has the unit velocity/length. It would be nicer to have used the absolute humidity (ρv) in place of q, in which case the moisture convergence would have the sensible unit [kg m-3 s-1], clearly a moisture source strength. Be that as it may, use the Plymouth State Weather Center web site to generate the moisture convergence field on the 700 hPa level over Western Canada at 12Z on 20 June 2013 (the unit will be knots m-1).
Note: Computing or measuring divergence always entails finding the small difference between large numbers, and as such, is a legendary difficulty. Some of the features plotted on your chart may in fact be artifices. The quality of a flux divergence field is to some extent dependent on the quality of the velocity divergence field, and that (in turn) to some extent linked to the density of upper air observations (radiosonde stations) informing the underlying weather model. Secondly, recall that unresolved terrain detail may have played a role in the precipitation pattern, so that while suggestive, a map like this is not definitive.
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The storm did cause chaos in the eastern U.S. and Canada, but perhaps the most prominent news item was that much less snow fell in New York City than had been forecast. From the New York Times: "The blizzard warning was canceled quickly for New York. The so-called March Madness storm did not quite live up to its name. But for air travelers, in particular, the storm hype resulted in woes, rebookings and a bit of creative thinking. Many airlines started grounding flights well before the weather system moved through the Northeast, keeping planes away from a region that was expected to be paralyzed. In total, more than 6,000 flights were canceled across the United States on Tuesday, including all American Airlines flights to New York City's three main airports" (Zach Wichter, 14 March)
Now with ω700 = -4 Pa s-1 (there were cores of even higher ω) and density ρ=700/(287 x 278.15)=0.877 kg m-3 we deduce that w=-ω/(ρ g) = +0.46 m s-1 and so the resolved vertical vapour flux density (according to this calculation) is
E=⟨w⟩ ⟨ρv⟩ = 3.1 x 10-3 kg m-2 s-1. To convert this vapour flux density to a velocity, we divide by the density of liquid water, i.e. by 1000 kg m-3. This gives us E= 3.1 x 10-6 m3 m-2 s-1 (so we have the unit: [m s-1]). To converting this to a velocity in mm/hr we multiply by 1000 (m to mm) and by 3600, so, E= 11 mm hr-1. It is common to multiply liquid water depths by 10 to get snow depths, thus 11 cm/hr of snow.
Just for interest, here is the analysed 24h cumulative precip (valid 12Z Wed. 15 March), which you might compare against the forecast precipitable water. It is important to understand that this computation -- for the resolved vertical vapour flux E -- is by no means necessarily equal to the actual precipitation rate at ground. Neither should the precipitable water [mm] be regarded as being a forecast for actual precipitation (over 6h? 12h? 24?). That said, strong precipitation rates are unlikely to be seen in regions where the precipitable water is low (dry air) and where the air aloft, as well as being quite dry, is not in a state of rapid ascent. Convective (summer storm) rainfall events are a possible exception to this statement.
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Available guidance:
Data for forecast verification:
Observations:
Answers to heat budget questions (angle bracket denotes average): (1) surface kinematic heat flux ⟨w'θ'⟩0 ≈ 0.28 K m s-1; (2) ∂⟨θ⟩ / ∂t ≈ 0.6 K hr-1.
Added after class: Guidance available from the GEM RDPS prog initialized 00Z Thurs 2 March (mostly 120h forecasts; the RDPS run initialized at 12Z Thurs 2 March had not completed in time to be used for this task):
Actual conditions around Winnipeg at 00Z on Tuesday 7 March 2017:
Please hand in a paragraph summarizing what this exercise has demonstrated (or what you conclude from it).
Added after class: Example
For simplicity, let's label the morning sounding T1i (i=1...8) where pi, zi are the corresponding pressure and height. Now on the afternoon sounding θ is constant (we'll take θ=303 K). Thus, for each pi of the morning sounding we are able to compute an afternoon temperature T2i (i=1...8), where each T2i is obtained by using (rearranging) the equation that defines θ (in this equation, for each pi we know θ, so rearrange to get T2i).
Now for each pi (which corresponds to height zi) compute ΔTi = T2i - T1i and the local density ρi.
Finally, compute the total heat added by the approximation Qi Δt = Σi ρi cp ΔTi (zi+1 - zi ), with the summation (Σi) running from =1...7.
Answers:
Some of the guidance available at the time:
JDW's Summary: the forecast thickness increase (24 dam or 12oC) implies the lower stratosphere should be considerably milder; surface temperature in the minus 5 to minus 15o bracket; sunny, with possible patchy high cloud; light SW wind; no precip.
Actual conditions in C. Alberta at 18Z Saturday 14 January (incl. RDPS 0h prog):
Link to Earth & Atmospheric Sciences home page.
