Genesis and persistence of Hurricane Nadine (2012) provides multiple opportunities for in situ sampling by unmanned aircraft Timothy J Dunkerton & co-authors Mike Montgomery, Scott Braun, Blake Rutherford, Zhuo Wang, Deanna Hence Gabe Susca-Lopata, Heather Archambault, Lou Lussier III, Sergio Abarca, Mark Boothe

MRG pouch products: Nadine 2012 (pre-genesis only) Black to red: hrs lead Circle = ECMWF / Square = GFS / Diamond = UKMET / Triangle = NOGAPS / Inverted triangle = HWGEN / Open circle = consensus Chronometer dial “time” = forecast initialization day relative to first day of tracking extrapolation P24L

Black to red: hrs lead extrapolation MRG pouch products: Nadine 2012 (pre-genesis only) Circle = ECMWF / Square = GFS / Diamond = UKMET / Triangle = NOGAPS / Inverted triangle = HWGEN / Open circle = consensus Chronometer dial “time” = forecast initialization day relative to first day of tracking P24L

MRG pouch products: Nadine 2012 (all models) P24L

MRG pouch products: Nadine 2012 (consensus) P24L

26 K SST at crossover point 0917 (top) & 0929 (bottom)

/22/00Z SUBTROPICAL STORM /23/15Z TROPICAL STORM /22/00Z LOW /22/06Z LOW /22/12Z LOW /22/18Z LOW /23/00Z TROPICAL STORM /23/06Z TROPICAL STORM /23/12Z TROPICAL STORM /23/18Z TROPICAL STORM Nadine rediscovered by HS3, then NHC Re-intensification into early October, final advisory 87A (real-time), 96 (best track) Real-time Best track AV-6 →

Flight Times As a Function of Nadine’s Life Cycle HS3 Flights Hurricane Tropical Storm Post-tropical low 3/31/ st Conf. on Hurricanes and Tropical Meteor. 8

600 hPa RH + TPW EastWest RH (%) Temp Anomaly (K) V (m/s) Nadine Vertical Structure (Sept 22-23) 400 hPa Temperature 600 hPa Relative Humidity

Critical layer theory for steady waves in shear exploits the separation of scales between outer and inner solutions: the wire frame is already present, and absolute vorticity is advected passively around the cat’s eye. Emergent waves implies growth of the wire frame in space & time, including the separatrix or unstable manifold that is responsible ultimately for protection of the pouch. Pairing and combination of two or more adjacent vortex pouches is possible on a time scale longer than the slower time scale of critical layer theory. Nadine (2012) combines three pouches: P23L, P24L and P25L. Dunkerton, Montgomery & Wang, 2009 ACP, Figure 1 amended (heavy arrows), wave-relative frame. Ideas relevant to the genesis of Nadine 2012

Hypothetical conversation at NASA HQ Jack Kaye: We think it’s really important to know if Atlantic hurricanes are affected by the Saharan Air Layer, and if our investment in these aircraft and their instrumental payloads has been able to address the issue. Scott Braun: Yes, Jack, we understand the importance of the issue. Some of our flights and retrospective modeling suggest that SAL aerosol has affected the storms sampled, and -- by the way -- dry air as well. Jack: How so? Scott: Well, it’s not just dust that matters, but the fuel that drives hurricanes, namely water vapor, and when the air nearby is dry, you’re likely to have negative impacts on storm development and intensity. In some cases, we’ve been able to show that dry air is getting in there. Jack: Getting in where? …into the clouds? Into the core? Into the outer bands? Into the pouch? Inner pouch region? Outer pouch region? The infamous “where is there” question.

Measurements are meaningful only in the context of their location within the evolving flow. – What air mass was sampled at the particular location of the dropsonde? – If laminae are present in the sounding, are multiple air masses responsible, arriving from different locations? – How did moist convection nearby affect the measurements? – Ideal platform samples the same disturbance over consecutive days (moistening, structural & intensity change). Multiple scales & remote oceanic location require airborne sampling. – Meso-α flight pattern planned a day or more in advance, pouch location & multi-model short-range forecast skill, deterministic & ensemble, in situ data denial for retrospective evaluation, Lagrangian history of pouch composition – Meso-β (proto-)vortex structure, horizontally & vertically, relevant UT/LS phenomena, minor adjustments to flight plan in real time – Meso-γ cloud population, avoidance maneuvers, cloud entrainment & detrainment meso-α km / meso-β km / meso-γ 2-20 km Philosophy An objective coordinate system is required based on the phenomenon itself: “center” for proto-vortex / “saddle” for pouch boundary / unique C px & C py for each; applies pre- & post-genesis, mature hurricane the ultimate “pouch”, nesting of LCS’s.

Tim Gabe Centering in real time: visual, intuitive, seat-of-the pants 600 hPa Relative Humidity

Objective coordinate system for interpretation of airborne measurements & satellite imagery Rotational components of horizontal velocity obtained from a Helmholtz decomposition of retrospective re-analyses. – Vortex center – Size & orientation – Anisotropic structure – Vertical alignment Translating stream function with spatially/slowly varying background Helmholtz flow removed – Innermost pouch contours of stream function surround vortex center. – Outermost pouch contours of stream function intersect relevant hyperbolic points or translating “saddles”. – Accuracy of trajectories in tightly curved flow improved by elimination of systematic error. Translating critical point functions assist center & saddle determination – Centers are characterized by a quasi-rectangular patch, positive Jacobian. – Saddles likewise, but w/ negative Jacobian, tend to collapse along a curve approximating the unstable manifold (tracer “front”).

Objective coordinate system for interpretation of airborne measurements & satellite imagery Rotational components of horizontal velocity obtained from a Helmholtz decomposition of retrospective re-analyses. – Vortex center – Size & orientation – Anisotropic structure – Vertical alignment Translating stream function with spatially/slowly varying background Helmholtz flow removed – Innermost pouch contours of stream function surround vortex center. – Outermost pouch contours of stream function intersect relevant hyperbolic points or translating “saddles”. – Accuracy of trajectories in tightly curved flow improved by elimination of systematic error. Translating critical point functions assist center & saddle determination – Centers are characterized by a quasi-rectangular patch, positive Jacobian. – Saddles likewise, but w/ negative Jacobian, tend to collapse along a curve approximating the unstable manifold (tracer “front”).

Ozone Centers & saddles in retrospective analysis: translating stream function Operational ECMWF 25 km, 700 hPa, 48 h leading up to Latitude tracer

Objective coordinate system for interpretation of airborne measurements & satellite imagery Rotational components of horizontal velocity obtained from a Helmholtz decomposition of retrospective re-analyses. – Vortex center – Size & orientation – Anisotropic structure – Vertical alignment Translating stream function with spatially/slowly varying background Helmholtz flow removed – Innermost pouch contours of stream function surround vortex center. – Outermost pouch contours of stream function intersect relevant hyperbolic points or translating “saddles”. – Accuracy of trajectories in tightly curved flow improved by elimination of systematic error. Translating critical point functions assist center & saddle determination – Centers are characterized by a quasi-rectangular patch, positive Jacobian. – Saddles likewise, but w/ negative Jacobian, tend to collapse along a curve approximating the unstable manifold (tracer “front”).

Centers & saddles in retrospective analysis: translating critical point functions ERA-Interim, 650 hPa 30 h leading up to Centers: filled / saddles: open / colors: blue (steady) to red (unsteady) / contours: red (cpx constant) & blue (cpy constant)

Translating critical points at lower & upper levels, 9/10/06Z hPa hPa LN = elliptic center (near Nadine only) LL = hyperbolic saddle (all shown)

Sorry about mid-term gaps, they are due to unsteadiness at peak intensity, relaxed constraint ok! red: u ζ black: v ζ filled: max open: min

Centers & saddles, method 1: rotational velocity Simple structure constraint: a vortex core with or without skirt should have a well-defined tangential velocity maximum at some radius, and some type of axisymmetry, whether circular, elliptical, or polygonal. The smoothness of rotational components of horizontal velocity lies between that of stream function (smoother but not invariant) and vorticity (invariant but noisier), the latter subject to advective rearrangement and non-advective fluxes associated with moist convection. In the genesis sequence, aggregation of vorticity is expected to yield a simple structure, but superposition of multiple waves and intersection perhaps of two storm tracks implies the possibility of multiple rotational velocity extrema within an emerging pouch structure. Emerging pouch → Simple rotational velocity structure → Vorticity monopole or annulus Parent wave pouchProto-vortex near pouch center extrema are invariant under spatially constant translation

Method 1 criteria & preliminary findings Identify significant local extrema of horizontal rotational velocity components: – Within a nearby grid of data, e.g., 15 degrees on a side – At least one standard deviation away from average on this grid – Nearest to nominal center, first guess from MRG pouch products – Cyclonic flow required: westerly equatorward (easterly poleward) of grid center, poleward east (equatorward west) of grid center – Revised grid center obtained from average of previous grid center and whatever significant extrema are obtained, up to four May not work well pre-genesis if multiple circulations are present and/or weak Identifies the resolved RMTW even when larger extrema nearby but outside Non-circular vortices often observed MRG pouch products, usually at 700 hPa, provide suitable first guess for 925 hPa vortex center, iteration yields minor improvement & converges rapidly Alternative reference levels hPa work equally well (or poorly) For warm-core systems we prefer to view the world nearby with respect to a low level such as 925 hPa, expansion and displacement of circulation w/ height. extrema are invariant under spatially constant translation