A scale-independent analysis tool of vortex structures: Proposed application to precipitation events

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precipitation events Lisa Schielicke Institute

Germany c NSSL c Doswell and Burgess (1993) c

3 s 1 300 km/10 4 s 1 1000 km/10 5 s 1 Typical

1 A scale-independent analysis tool of vortex structures: Proposed application to precipitation events Lisa Schielicke Institute of Meteorology, Free University Berlin, Germany c NSSL c Doswell and Burgess (1993) c NASA c NASA Modis L/ζ 100 m/10 0 s 1 10 km/10 3 s km/10 4 s km/10 5 s 1 Typical scales of horizontal length L and vorticity ζ of different vortices.

pressure system on southern hemisphere: (a) undisturbed, (b) westerly flow U=const. added, (c) 2 U added, (d) 3 U added.

2 Scale-independent analysis tool of vortex structures 2/10 Problem: What is a vortex? Pressure-based vortex identification methods might fail in different background flows: Relative vorticity at different model layers, NCEP reanalysis data: Low pressure system on southern hemisphere: (a) undisturbed, (b) westerly flow U=const. added, (c) 2 U added, (d) 3 U added. Dot: vorticity center, L: pressure minimum Fig.1 of Sinclair, M.R., 1994: An objective cyclone climatology for the Southern Hemisphere. Mon. Wea. Rev., 122(10), ; c American Meteorological Society. Used with permission. Fixed vorticity thresholds might fail (especially at upper levels).

3 Scale-independent analysis tool of vortex structures 2/10 Problem: What is a vortex? Pressure-based vortex identification methods might fail in different background flows: Relative vorticity at different model layers, NCEP reanalysis data: An accepted [objective, mathematical] definition of a vortex is still lacking Jeong&Hussain,J Fluid Mech,1995. Low pressure system on southern hemisphere: (a) undisturbed, (b) westerly flow U=const. added, (c) 2 U added, (d) 3 U added. Dot: vorticity center, L: pressure minimum Fig.1 of Sinclair, M.R., 1994: An objective cyclone climatology for the Southern Hemisphere. Mon. Wea. Rev., 122(10), ; c American Meteorological Society. Used with permission. Fixed vorticity thresholds might fail (especially at upper levels).

4 Scale-independent analysis tool of vortex structures 3/10 W k -method Kinematic vortex identification What is the size and intensity of a vortex? Schielicke, Névir & Ulbrich, 2016: Kinematic vorticity number - a tool for estimating vortex sizes and circulations. Tellus A Schielicke, 2017: Scale-dependent identification and statistical analysis of atmospheric vortex structures in theory, model and observation. Freie Universität Berlin, PhD-thesis

5 Scale-independent analysis tool of vortex structures 3/10 W k -method Kinematic vortex identification What is the size and intensity of a vortex? Schielicke, Névir & Ulbrich, 2016: Kinematic vorticity number - a tool for estimating vortex sizes and circulations. Tellus A Schielicke, 2017: Scale-dependent identification and statistical analysis of atmospheric vortex structures in theory, model and observation. Freie Universität Berlin, PhD-thesis Inspecting the wind field u(r0 + δr, t) in the close environment of point r0 (1. order Taylor series expansion): u(r0 + δr, t) = u(r0, t) +δr u(r0, t) }{{}}{{} translation strain&rotation with u = S + Ω S: symmetric strain-rate tensor, Ω: antisymmetric vorticity tensor

6 Scale-independent analysis tool of vortex structures 3/10 W k -method Kinematic vortex identification What is the size and intensity of a vortex? Schielicke, Névir & Ulbrich, 2016: Kinematic vorticity number - a tool for estimating vortex sizes and circulations. Tellus A Schielicke, 2017: Scale-dependent identification and statistical analysis of atmospheric vortex structures in theory, model and observation. Freie Universität Berlin, PhD-thesis Inspecting the wind field u(r0 + δr, t) in the close environment of point r0 (1. order Taylor series expansion): u(r0 + δr, t) = u(r0, t) +δr u(r0, t) }{{}}{{} translation strain&rotation with u = S + Ω S: symmetric strain-rate tensor, Ω: antisymmetric vorticity tensor Vortex definition based on the kinematic vorticity number W k after Truesdell (1953, J.Ration.Mech.Analysis, 2, ): W k = Ω S < 1 : no vortex = 1 : pure shear > 1 : a vortex

Scale-independent analysis tool of vortex structures 4/10 W k -method On the meaning of W k = 1 1 + (a) 10 m/s 10 m/s 2 + (b)

line). Blue box indicates the excerpt plotted in (a) und (b).

7 Scale-independent analysis tool of vortex structures 4/10 W k -method On the meaning of W k = (a) 10 m/s 10 m/s 2 + (b) Wk=1 Wk=1 y (km) Wk > 1 Wk > 1 Fig: Superposition of two cyclones: Pressure (black contours) and W k = 1 contour (thick black line). Blue box indicates the excerpt plotted in (a) und (b). Streamlines (blue) and wind field (green) around the locations denoted with (a) 1 on the W k =1 contour and (b) 2 inside the region of W k > 1. Adapted from Schielicke,Névir,Ulbich,Tellus A,2016. x (km)

8 Scale-independent analysis tool of vortex structures 5/10 W k -method Implementation & application UTC, NCEP reanalysis, res.: 2.5 Geopot. height/ vorticity in 500 hpa: Fig: Geopot. height contours (black, every 8 gpdm) and relative vorticity (shaded, in 1/s); UTC

9 Scale-independent analysis tool of vortex structures 5/10 W k -method Implementation & application UTC, NCEP reanalysis, res.: 2.5 Geopot. height/ vorticity in 500 hpa: Field of Wk (dimensionless) in 500 hpa: Fig: Geopot. height contours (black, every 8 gpdm) and relative vorticity (shaded, in 1/s); UTC Fig: Kinematic vorticity number Wk considering the sign of vorticity in 500 hpa, UTC

10 Scale-independent analysis tool of vortex structures 5/10 W k -method Implementation & application UTC, NCEP reanalysis, res.: 2.5 Geopot. height/ vorticity in 500 hpa: Field of Wk (dimensionless) in 500 hpa with ( Wk =1)-contours: Fig: Geopot. height contours (black, every 8 gpdm) and relative vorticity (shaded, in 1/s); UTC Fig: Wk considering the sign of vorticity in 500 hpa, UTC; (blue: Wk = 1, red: W k = 1)

11 Scale-independent analysis tool of vortex structures 5/10 W k -method Implementation & application UTC, NCEP reanalysis, res.: 2.5 Geopot. height/ vorticity in 500 hpa: Vortex mask based on ( Wk =1)-contours: Fig: Geopot. height contours (black, every 8 gpdm) and relative vorticity (shaded, in 1/s); UTC Fig: Vortex mask in 500 hpa, UTC; (gray=1 for W k > 1; white=0 for W k 1)

12 Scale-independent analysis tool of vortex structures 5/10 W k -method Implementation & application UTC, NCEP reanalysis, res.: 2.5 Geopot. height/ vorticity in 500 hpa: Vortex field in 500 hpa (=Mask Vorticity field): Fig: Geopot. height contours (black, every 8 gpdm) and relative vorticity (shaded, in 1/s); UTC Fig: Vorticity (in 1/s) in the field of Wk > 1; isolines of geopotential height (in 8 gpdm) in 500 hpa, UTC

13 Scale-independent analysis tool of vortex structures 5/10 W k -method Implementation & application UTC, NCEP reanalysis, res.: 2.5 Geopot. height/ vorticity in 500 hpa: Vortex field/geopotential height in 500 hpa, local vorticity extrema: Fig: Geopot. height contours (black, every 8 gpdm) and relative vorticity (shaded, in 1/s); UTC Fig: Vorticity (1/s) in the field of Wk > 1, 500 hpa, UTC; (+: vorticity maxima, -: vorticity minima)

14 Scale-independent analysis tool of vortex structures 6/10 W k -method Implementation & application UTC, NCEP reanalysis, res.: 2.5 Geopot. height/ vorticity in 500 hpa: Vortex field/geopotential height in 500 hpa, local vorticity extrema: Fig: Geopot. height contours (black, every 8 gpdm) and relative vorticity (shaded, in 1/s); UTC Fig: Vorticity (1/s) in the field of Wk > 1, 500 hpa, UTC; (+: vorticity maxima, -: vorticity minima)

15 Scale-independent analysis tool of vortex structures 6/10 W k -method Implementation & application UTC, NCEP reanalysis, res.: 2.5 Geopot. height/ vorticity in 500 hpa: Vortex field/geopotential height in 500 hpa, local vorticity extrema: Fig: Geopot. height contours (black, every 8 gpdm) and relative vorticity (shaded, in 1/s); UTC Fig: Vorticity (1/s) in the field of Wk > 1, 500 hpa, UTC; (+: vorticity maxima, -: vorticity minima)

16 Scale-independent analysis tool of vortex structures 6/10 W k -method Implementation & application UTC, NCEP reanalysis, res.: 2.5 Geopot. height/ vorticity in 500 hpa: Vortex field/geopotential height in 500 hpa, local vorticity extrema: Fig: Geopot. height contours (black, every 8 gpdm) and relative vorticity (shaded, in 1/s); UTC Fig: Vorticity (1/s) in the field of Wk > 1, 500 hpa, UTC; (+: vorticity maxima, -: vorticity minima)

Scale-independent analysis tool of vortex structures 7/10 W k -method 3d vortex visualization Visualizing of 3d vortex structure with help of vorticity (ζ) isosurfaces Pressure level (z.b.

17 Scale-independent analysis tool of vortex structures 7/10 W k -method 3d vortex visualization Visualizing of 3d vortex structure with help of vorticity (ζ) isosurfaces Pressure level (z.b. 500 hpa) z ζ/w k -contour Pressure level (z.b hpa) (a) Mask of W k -number is determined for every horizontal field seperately and (if wanted) multiplied by another field (e.g. vorticity field) ζ-isosurface (b) Isosurfaces (e.g. for fixed vorticity values) are constructed by vertical stacking of the horizontal fields.

Scale-independent analysis tool of vortex structures 8/10 W k -method 3d vortex visualization (synoptic storm) 1999/12/02 12 UTC 1999/12/03 00 UTC 1999/12/03 12 UTC 1999/12/04 00 UTC 100 100 100 100

1000 0 1000 0 1000 0-10 -10-10 -10 70-20 70-20 70-20 70-20 60-30 60-30 60-30 60-30 50-40 (a) 50-40 (b) 50-40 (c) 50-40 (d) Lat [ ] Lon [ ] Lat [ ] Lon [ ] 1999/12/02 12 UTC 1999/12/03 00 UTC

100 200 300 400 500 600 700 800 30 900 30 900 30 900 30 20 20 20 20 10 10 10 1000 0 1000 0 1000 0-10 -10-10 70-20 70-20 70-20 60-30 60-30 60-30 (e) 50-40 (f) 50-40 (g) 50-40 (h) Lat [ ] Fig.

18 Scale-independent analysis tool of vortex structures 8/10 W k -method 3d vortex visualization (synoptic storm) 1999/12/02 12 UTC 1999/12/03 00 UTC 1999/12/03 12 UTC 1999/12/04 00 UTC based on Wkmethod p [hpa] (a) (b) (c) (d) Lat [ ] Lon [ ] Lat [ ] Lon [ ] 1999/12/02 12 UTC 1999/12/03 00 UTC 1999/12/03 12 UTC 1999/12/04 00 UTC Lat [ ] Lon [ ] Lat [ ] Lon [ ] Time based on the pure vorticity field p [hpa] Lat [ ] Lon [ ] (e) (f) (g) (h) Lat [ ] Fig. (3d visualization): Isosurfaces of vorticity ([1, 3, 5] 10 5 s 1 ). Lon [ ] (a)-(d) Vorticity plotted in the field of Wk in Schielicke,Névir,Ulbich,Tellus A, Lat [ ] Lon [ ] Lat [ ] Lon [ ] > 1; (e)-(h) vorticity-isosurfaces. Published

Scale-independent analysis tool of vortex structures 9/10 W k -method 3d vortex visualization (simulated supercell) 3d visualization of vortex tubes in a

(km) Y (km) X (km) Fig.: Vertical development of supercell simulated with WRF.

19 Scale-independent analysis tool of vortex structures 9/10 W k -method 3d vortex visualization (simulated supercell) 3d visualization of vortex tubes in a simulated supercell Distance between model levels 500 m Model levels Y (km) (a) t=15 min (b) t=30 min (c) t=45 min (d) t=60 min X (km) Y (km) X (km) Y (km) X (km) Y (km) X (km) Fig.: Vertical development of supercell simulated with WRF. Isosurfaces of smoothed vorticity ([±1, ±5] 10 3 s 1 ) in the field of Wk ast > 1. Red: cyclonic, blue anticyclonic; thick, (e) black t=75 arrow min indicates (f) t=90 cell motion. min From (g) t=105 Schielicke min (2017, (h) PhD-thesis). t=120 min

Scale-independent analysis tool of vortex structures 10/10 Conclusion The W k -method captures well the vortex structures on different scales, in different resolutions and at

This figure was originally presented at a talk entitled Vortex identification and interactions across the scales at the European Conference on Severe Storms (ECSS) 2017 in Pula,

20 Scale-independent analysis tool of vortex structures 10/10 Conclusion The W k -method captures well the vortex structures on different scales, in different resolutions and at different height levels. It can be applied in various ways... Contact: lisa.schielicke@met.fu-berlin.de NCEP, 2.5 res. CFSR, 0.5 res. COSMO, 2.8 km res. This figure was originally presented at a talk entitled Vortex identification and interactions across the scales at the European Conference on Severe Storms (ECSS) 2017 in Pula, Croatia with co-authorship of Christoph Gatzen. The W k -method will be implemented as a plugin analysis tool soon on: The FU Berlin Evaluation System (Freva) is free of charge after registration.

Southern Hemisphere Storminess under recent and anthropogenic climate conditions based on a multi model ensemble analysis

Southern Hemisphere Storminess under recent and anthropogenic climate conditions based on a multi model ensemble analysis Jens Grieger G.C. Leckebusch, M. Schuster, U. Ulbrich (contact: jens.grieger@met.fu-berlin.de)