Essence of Mid-latitude Weather Systems
Transcript of 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