essence of mid-latitude weather systems

Huw C. Davies

Institute for Atmospheric and Climate Science, ETH Zurich

Essence of

Mid-latitude Weather Systems ?

“Dynamical Insights into Weather & Climate”

Buys Ballot Symposium in honour of Sir Brian Hoskins, 2014 Medalist

KNAW, 23rd

June, 2014.

Characteristics of Fronts & Cyclones

Characteristics of Fronts & Cyclones

- exhibit significant case-to-case variability,

- posses a rich spatial structure, and

- occur irregularly

sic. complex and chaotic natural system.

… the most changeable and capricious of all of nature’s phenomena.

The latter, transient and intangible, evade every attempt to capture them

under the bridle of the law. H. von Helmholtz, 1876

The Challenge & the Science Setting circa 1970

Scale of the scientific challenge has long been well recognized :

AND YET the progress

in our fundamental understanding of the dynamics of weather systems

over the last four decades

has been remarkable, wide-ranging and profound.

SETTING ..

The Concept of Quasi-Geostrophy

- there are ‘physically consistent’ primary and secondary synoptic-scale flow components

a primary geostrophic component (vG) a secondary ageostrophic component (v

AG)

whose evolution is determined by required by, and that can be inferred from,

the geostrophic flow itself the geostrophic flow

..

ATMOSPHERIC DYNAMICS SYNOPTIC METEOROLOGY

Step I .

BEYOND Quasi-Geostrophy

& the Dynamics of Fronts

Step II

..

Quasi-Geostrophic Diagnosis

Step III & Synoptic-Scale Systems

…

PV Perspective & Dynamics

of mid-latitude weather systems

The BJH Sequel

CONCEPT

There is a physically consistent flow evolution with a more refined

“state of balance” than quasi-geostrophy

- semi-geostrophy & geostrophic momentum systems

DGM

(A)/Dt = {∂ /∂t + ((vG

+ vAG

).) } A IMPLICATIONS

(A) Idealized, but germane, physical settings

evolve ‘realistically’ to yield fronts

- captures the essence of frontogenesis

Beyond Quasi-Geostrophy

& the Dynamics of Fronts

BJH Step I

θ cross-section at t= 0

θ cross-section at t=75 hours ‘w’ cross-section

at t=75 hours

CONCEPT

There is a physically consistent flow evolution with a more refined

“state of balance” than quasi-geostrophy

- semi-geostrophy & geostrophic momentum systems

DGM

(A)/Dt = {∂ /∂t + ((vG

+ vAG

).) } A

IMPLICATIONS

(A) Idealized, but germane, physical settings

evolve ‘realistically’ to yield fronts

- captures the essence of frontogenesis

(B) Development of coherent frontal features

equates to a rapid physical scale contraction

and a distinctive spectral cascade

- local K.E spectrum α k -8/3

& local Enstrophy spectrum α k - !!!

Beyond Quasi-Geostrophy

& the Dynamics of Fronts

BJH Step I

CONCEPT

There is a physically consistent flow evolution with a more refined

“state of balance” than quasi-geostrophy

- semi-geostrophy & geostrophic momentum systems

DGM

(A)/Dt = {∂ /∂t + ((vG

+ vAG

).) } A

IMPLICATIONS

(A) Idealized, but germane, physical settings

evolve ‘realistically’ to yield fronts

- captures the essence of frontogenesis

(B) Development of coherent frontal features

connotes a notable physical scale contraction

and a distinctive spectral cascade

- local K.E spectrum α k -8/3

& local Enstrophy spectrum α k - !!!

(C) Refined “flow” system indicative of

both the nature of balanced large-scale flow

and the “validity” of quasi-geostrophy

Beyond Quasi-Geostrophy

& the Dynamics of Fronts

BJH Step I

Depictions of the error in “Semi-Geostrophy”

(Neglected terms/Coriolis term)2 at t= 75 hours

Quasi-Geostrophic Diagnosis

& Synoptic-scale Systems

BJH Step II

Quasi-Geostrophic Omega Equation

..

- prescribes the secondary ageostrophic vertical velocity field, (w) , required to maintain the primary geostrophic flow

N2(∇2H w) + fo

2 (∂2w/∂z2) = F

Pre-BJH

F = fo ∂ [(vG.∇H)ζg ]/∂z - ∇2

H [(vG.∇H)b ] Conventional Formulation

= 2 fo [(∂vG/∂z).∇H] ζg + D2

(∂e/∂z) Refined-Sutcliffe Formulation ..

D - total geostrophic flow deformation,

(∂e/∂z) - change of dilatation axis with height

..

BJH

F = 2 (∇H. Q) ‘Q-Vector’ Formulation ..

Q = - |H q*| { k∂v

G/∂s}

.

Viewed from an R Vector standpoint

= fo ∂ [(vG.∇H)q ]/∂z - ∇2 {(vG.∇H)b}/N2 ‘PV’ Formulation

Bridge between

Atmospheric Dynamics

& Synoptic Meteorology

Deformation term = D2 (∂e/∂z)

= - {D . S } sin 2(λ-ε) ..

with (D,ε) - def. & dilat. angle of the geostrophic

wind,

(S,λ) - def. & dilat. angle of the thermal wind,

THE CLASSICAL CHALLENGE .

Given the Height and Theta fields on a specified pressure surface,

assess qualitatively the “forcing” (and hence the preferred regions for ascent)

..

DIGRESSION – Postscript on the

‘Deformation term’ of the

refined Sutcliffe Formulation

Flow: Deformation Localized Baroclinic Zone

ASCENT

DESCENT

θ

(i) Omega Equation “Forcing” & Dynamics

BJH Step II

.

Thermal Wind Equation

Insistence on Its Maintenance

thermal wind advection of the geostrophic flow

Implication

Primary geostrophic flow acting alone has a self-destructive tendency.

Secondary ageostrophic flow is required to offset this effect.

Linkage of R to the Q-vector Formulation

.

F = 2 (∇H. Q) = 2 (curl R) ∫∫s (F ) ds α

(a) R relates directly to the three-dimensional ageostrophic circulation

(ii) R- Vector is seminal to QG flow dynamics

BJH Step II

α change of the wind

along the isentropes

(a) R relates directly to the three-dimensional ageostrophic circulation

(ii) R- Vector is seminal to QG flow dynamics

BJH Step II

Concept of “Thermal Wind Lines”

Lines everywhere tangential to the local orientation of the thermal “wind” (T = ∂vG/∂z )

i.e. aligned with isentropes and strength α baroclinicity

…

Quasi-Geostrophic Equation for TWL

DG {T }/Dt = + (T .∇H) vG - N2 {k∧∇H(w)}

Change following Distortion Modification by w-field

geostrophic flow (- amplification by lateral stretching

- deformation by reorientation)

c.f. Vortex lines: D {ω} /Dt) = + (ω.∇) v

Thus (i) T lines behave like geostrophic ‘material lines’ at the surface

(ii) Amplification and deformation accomplished by :-

(T .∇H) vG = R = [(∂vg/∂z).∇H] vG

..

(b) It relates intrinsically to distortion and turbulence of surface QG

Illustration of “material”

Line behaviour

Implication:

Geostrophic flow --> can itself embody a physical cascade to sub-synoptic scales

and onto geostrophic turbulence.

..

(a) R–vector intrinsic to a general (but pseudo) Omega Equation.

(iii) QG-Omega Equation outdated ? BJH Step II

ECMWF Output: 850hPa wind vector arrows and thermal field

Q-Vectors evaluated with full model fields. ECMWF Output: vertical velocity field &

..

(a) R–vector intrinsic to a general (but pseudo) Omega Equation.

(iii) QG-Omega Equation outdated ? BJH Step II

..

(b) QG-Omega Equation & Diabatic Heating

CHALLENGE

Given radar, satellite and surface rainfall data of :-

intensity, vertical profile, location of cloud-diabatic activities.

Either Adjust model distribution to the observations by

modifying model fields/heating instantaneously

or quasi-continuously

Or Accommodate stochastically.

DESIRED RESPONSE ?? QG- Response Unbalanced Response ?

PV Perspective

& Mid-latitude Weather Systems

BJH Step III

PV Perspective:

Discerned & Defined,

Refined & Extended,

Insightfully Exploited

CONSERVATION

PARTITION & INVERSION

Step III

Cold Warm

Potential Vorticity Perspective

PV Dynamics of isolated Cyclogenesis:

Interaction of a tropopause-level PV Anomaly

with a surface Front

D(PV)/Dt = 0

for adiabatic, frictionless flow

D(PV)/Dt α (∂Q/∂z)

with Q denoting rate of cloud-diabatic heating

∂Q/∂z < 0

∂Q/∂z > 0

Step III PV Perspective of a mature cyclone.

View from SW View from NE

PV@320K on January 16, 2002

Forecast - Analysis

FC96

Analysis

Step III Two Examples of the PV Perspective: ..

(i) PV & Forecast Error Growth

Equation for Forecast Error Growth:

+ Diabatic Effects …

Growth/Wave-Propagation Non-linear growth !!!!!!!!

AN FC hPa pvu

Examine Lagrangian History:

96 hour backward parcel trajectories from “Regions of large PV’ Error”

ORIGIN OF NEGATIVE “ERROR

related to the instigation / occurrence of deep moist ascent !!!

BUT

Two Examples of the PV Perspective: (i) Dynamics & Diagnosis of PV Error

Step III

Evolution of a Blocking Event

PVU PV on 320K

Two Examples of the PV Perspective: (ii) Dynamics of Atmospheric Blocks

Step III

Diagnosed ingredients of a realized Winter 05-06 Block

Observed /

ECMWF Analysis

Control

Simulation

Modified

Simulation

HYPOTHESIS Upstream anomalies in Atlantic SST and land surface temperature impact positively upon Block formation

Balanced Flow & Fronts

PV Perspective & Flow Development

SUMMARY

Omega Equation & Diagnosis of Synoptic Systems

BJH Research characterized by

ELEGANCE

&

RELEVANCE