Mesoscale Atmospheric Systems. Upper-level fronts. 13 and 20 March 2018 Heini Wernli. 13 March 2018 H. Wernli 1

Transcription

1 Mesoscale Atmospheric Systems Upper-level fronts 13 and 20 March 2018 Heini Wernli 13 March 2018 H. Wernli 1

2 Upper-level fronts Formation of fronts is favored by presence of quasi-horizontal boundaries: - the earth surface à surface fronts - the tropopause à upper-level fronts The tropopause: various definitions - thermal TP (WMO): change of temperature lapse rate - dynamical TP: the 2-pvu isosurface (some use pvu) - chemical TP: O 3 =100 ppbv, vertical gradient of O 3, We mainly use the dynamical TP, following the pioneering work of Reed and anielsen in the 1950ies. 13 March 2018 H. Wernli 2

3 Observation of front and tropopause on 15 Feb 1935 T θ - isothermal stratosphere - tropopause sloping down towards the north - deep frontal layer from surface to TP (enhanced hor & vert gradient of θ) cf. vertical extension of polar front - folding of TP at upper edge of front - note TP breaks to the south of front Bjerknes and Palmén March 2018 H. Wernli 3

4 Observation of front and tropopause on 5 Feb 1947 Isotherms Along-front geostrophic wind TP and frontal boundaries (dashed if not well defined) NY Cuba - folded TP is replaced by break region - front is strong throughout lower/middle troposphere but becomes weak in UT - front associated with strong cyclonic shear of along-front geostrophic wind - cyclonic shear zone extends into the lower stratosphere, weakens near TP - wind maximum at TP level, above intense front Palmén and Nagler March 2018 H. Wernli 4

5 Observation of front and tropopause on 9 Nov 1949 Potential temperature Wind speed TP and frontal boundaries - frontal layer extends into the lower stratosphere (with reversed temp. gradient) not confirmed by later obs. - near jet core frontal zone is solely defined by very strong cyclonic wind shear note that European sonde network was denser than over the US Hannover Berggren 1952 Valencia 13 March 2018 H. Wernli 5

6 Observation of front and tropopause over US in 1950ies isotherms & along-front geostrophic velocity isentropes & PV 20 = 2 pvu - TP joins the boundaries of the frontal zone - hypothesis: upper-level fronts result from TP folding process - stratosphere-troposphere exchange occurs in frontal zones with stratospheric air in upper part and tropospheric air in lower part of front Reed and anielsen March 2018 H. Wernli 6

7 Concepts of upper-level fronts and tropopause folds Bjerknes and Palmén 1937Palmén and Nagler 1947 Berggren 1952 Reed and anielsen 1959 Reed and anielsen March 2018 H. Wernli 7

8 What is the origin of upper-level fronts? Previous to Reed and anielsen (1959) - upper-level fronts form due to confluence of polar and tropical air à mainly deformation frontogenesis t n: direction perpendicular (normal) to front After Reed and anielsen - upper-level fronts form as a response to tropopause folding à mainly tilting frontogenesis ( transport of stratospheric stratification into upper troposphere ) 13 March 2018 H. Wernli 8

9 Upper-level front observed by radiosondes and aircraft wind speed and θ PV ( 200 = 2 pvu ) Shapiro March 2018 H. Wernli 9

10 Upper-level front observed by radiosondes and aircraft x (into plane) y (toward cold air) absolute momentum m (m,θ) coordination grid Shapiro March 2018 H. Wernli 10

11 Concept of quasi two-dimensional fronts Consider elongated front extended along x-axis Flow along the front is assumed to be in geostrophic balance, i.e., u = u g Flow in across-front direction has ageostrophic components (v ag, -ω) This is the basis of the so-called geostrophic momentum approximation, and of the semi-geostrophic theory of fronts 13 March 2018 H. Wernli 11

12 Absolute momentum efinition: Absolute geostrophic vorticity vector lies along lines of constant m: thermal wind relationship: gradient of m in (y,p) plane defined as (0,dm/dy,-dm/dp) i.e., derivatives of m related to vertical component of abs. vorticity and baroclinicity 13 March 2018 H. Wernli 12

13 PV in quasi 2-d frontal zones efinition (in pressure coordinates): PV = -g ζ θ (Ertel PV in pvu) P = - ζ θ (frequently used in the 1980ies) P P 2 = + ζ g2 2 θ (because of definition of 2) = ( ) = = (Jacobian) = 13 March 2018 H. Wernli 13

14 Prognostic equations absolute vorticity t crossfront thermal wind balance t t t static stability 13 March 2018 H. Wernli 14

15 Sawyer Eliassen eq. for transverse ageostrophic circulation Retain thermal wind balance à r.h.s. of 2 nd and 3 rd equation must be equal à express ageostrophic terms with streamfunction à linear, 2 nd order partial differential equation with variable coefficients forcing = geostrophic flow + friction + diabatic heating 13 March 2018 H. Wernli 15

16 Sawyer Eliassen eq. for transverse ageostrophic circulation S-E equation is elliptic if PV is positive in the entire domain: Elliptic PE: streamfunction is uniquely determined by forcing term Usually: pos. values of forcing à negative ψ à thermally direct circulation (cold air sinking, warm air rising à frontolytic) neg. values of forcing à positive ψ à thermally indirect circulation (cold air rising, warm air sinking à frontogenetic) 13 March 2018 H. Wernli 16

17 Sawyer Eliassen eq. for transverse ageostrophic circulation Creation of westerly / easterly geostrophic flow above / below minimum / maximum of streamfunction: /t u g = f v ag 13 March 2018 H. Wernli 17

18 Sawyer Eliassen equation: comparison with QG version As above: geostrophic momentum approximation QG version t t t t t t t t 13 March 2018 H. Wernli 18

19 Sawyer Eliassen equation: comparison with QG version As above: geostrophic momentum approximation QG version identical forcing terms in QG: circulation cannot tilt from vertical (no mixed-derivative term) ellipticity condition in QG: static stability > 0: 13 March 2018 H. Wernli 19

20 Sawyer Eliassen equation: forcing term many different formulations: evaluate forcing from solenoids of isolines of u g and v g in (y,p) sections evaluate forcing from solenoids of isolines of u g and θ on p-levels form used in large-scale dynamics lecture course, Q 2 = 13 March 2018 H. Wernli 20

21 Forcing due to confluence and horizontal shear Confluence forcing: Horizontal shear forcing: 13 March 2018 H. Wernli 21

22 Exercise: Identify transverse ageostrophic circulation pattern pure confluence & diffluence pure horizontal shear thick lines: geopotential height thin lines: isentropes dashed lines: along-front geostrophic wind arrow: cross-front ageostrophic wind at level of maximum wind +/- signs: sense of mid-tropospheric vertical motion ω 13 March 2018 H. Wernli 22