Aorangi (Mt. Cook) we typically view the state of the troposphere on "isobaric surfaces" (surfaces of constant pressure) rather

Transcription

1 Ch3 (ctd.) EAS270_Ch3_BehaviourAtmos_B.odp JDW, EAS UAlberta, last mod. 19 Sept Atmospheric "behaviour" Aorani (Mt. Cook) "ride" we typically view the state of the troposphere on "isobaric surfaces" (surfaces of constant pressure) rather Fi 3.12 than surfaces of constant heiht features in the "heiht field" include "closed lows and hihs", as well as "trouhs" and "rides" (e.. Fi 11.12)

2 Preamble to Sec 3.5 rides and trouhs on an isobaric surface 2/9 wind "follows" heiht contours upper lows tend to be better defined than the hihs weak radients at low latitudes meanderin airstreams (waves in the upper flow) TROUGH closed upper lows RIDGE Fi 3.22b

3 Preamble to Sec 3.5 rides and trouhs on an isobaric surface as you move perpendicularly away from the trouh axis, heihts rise as you move perpendicularly away from the ride axis, heihts fall contour interval: 6 dam 3/9 The heiht contour interval is 6 dam for the 850, 700 and 500 hpa surfaces; but it is 12 dam for the 250 hpa surface. secondary field (dashed line): "thickness" (which we will presently define) Fi 3.22b (blowup)

4 Sec 3.5 The hypsometric equation 4/9 ΔP = ρ Δz P = ρ Rd T v z z2 eliminate density dp P = dz Rd T v (Eqn 3.10) "the (rate of) chane in pressure with heiht is reater in cold air than it is in warm air" z1 P Note: rather than use the "finite difference notation" here, I have chosen to use the derivative symbol d. This is because I want to express the hydrostatic law in a form that applies at each and every point, whereas if the heiht increment were finite (denoted z rather than dz) I'd need Tv to be an averae over the interval. This distinction is made here only to avoid any discomfort for those needin the calculus to be riorous. We now interate upwards from heiht z1 to heiht z2, usin the first mean value theorem of calculus (steps not shown): [ R d T v Δ z z 2 z1 = ] P1 P2 (Eq 3.11) "the thickness of an atmospheric layer is the difference in heiht between two pressure surfaces" (that bound it). It is controlled by the layer's averae (virtual) temperature

5 Sec 3.5 Applyin the hypsometric equation 5/9 Suppose that at 00 UTC in Edmonton** on a certain day the pressure at round level was P=935 hpa and that the averae value of the temperature below the 850 hpa isobaric surface was -15oC: compute the heiht above round of the 850 hpa surface (nelect the distinction between T and Tv, for at these temperatures the mixin ratio r is very small). Δ z z2 z1 = [ Rd T v ] P1 P2 **Edmonton is about 700 m ASL (700 m above sea level), so surface pressures are much lower than the nominal 1000 hpa (=100 kpa = 105 Pa) fiure for pressure at sea level

6 Sec 3.5 Applyin the hypsometric equation 6/9 Let P1 = 850 hpa, P2 = 700 hpa. Suppose that layer mean Tv= -15oC at A and layer mean Tv= 5oC at B. What is the hpa thickness at A and at B? [ R d T v Δz = ] 850 = T v x = 5.68 T v 700 Δ z A =5.68 ( ) = 1466 m Δ z B=5.68 ( ) = 1580 m A B o T v = 15 C o T v =5 C (averae values from 850 hpa to 700 hpa) Fi 3.13

7 Sec 3.5 Usin the hypsometric equation to compute sea level pressure 7/9 Aain supposin that at 00 UTC in Edmonton on a certain day the pressure at round level was P=935 hpa, compute sea level corrected surface pressure (MSLP) P0, adoptin a value of -15oC for the temperature of the (fictitious) air column down to sea level: Δ z z Edmonton [ Rd T v 0 = 700 m= P = = x P0 = exp [ x 10 2 ] = Fi 3.15 ] P0 P0 P0 287 x( ) = =7552 P P 0 = x 935 = hpa

8 Sec 3.5 Thickness as surroate for mean layer temperature [ R d T v Δ z z 2 z1 = fix P1=1000, P2=500 hpa so Δ z [ m] = 20 T v ] 8/9 P1 P2, then or Rd P1 =20.3 P2 Δ z [dam] = 2 T v a 2 dam increase in layer mean thickness corresponds to a 1 K increase in mean temperature Fi 3.22a

9 Thickness contours secondary field on the 500 hpa isobaric surface 9/9 "thickness" from 1000 to 500 hpa, a surroate for mean temperature of the lower troposphere dam thickness band hihlihted by fill Manitoba storm wrapped cold air southward throuh Saskatchewan Fi 3.22b (blowup)

10 Close-packed isobars over Edmonton -- CMC surface analysis, 18Z Sunday 18 Sept explain it's bein a windy day

11 Lecture of 19 Sept. how to visualize an isobaric surface trouhs, rides, closed lows & hihs "toporaphy" of the isobaric surface the hypsometric eqn usin hypsometric eqn to define MSLP (sea-level corrected pressure) it is common on weather charts to display contours of hpa thickness as a surroate for the mean temperature of the lower troposphere