Asian monsoon - an important pathway into the stratosphere ?

Asian monsoon - an important pathway into the stratosphere ?

Paul Konopka

Forschungszentrum J ¨ulich, Germany,

Institute for Energy and Climate Research - Stratosphere (IEK-7) P.Konopka@fz-juelich.de

Outline

Motivation - why should we care about the Asian Summer Monsoon (ASM)

Modeling of transport and chemistry with CLaMS:

Lagrangian view transport

numerical diffusion versus physical mixing entropy (potential temperature) as vertical coordinate

CLaMS: some applications

ASM as a pathway of transport into the Tropical Tropopause Layer (TTL)

Conclusions

Monsoon in the tropical troposphere

...is defined as seasonal reversing wind accompanied by corresponding changes in precipitation associated with asymmetric heating of land and sea (Wikipedia)

Tropospheric cyclone drives the anticyclone above

Summer convection + Coriolis force + Kelvin’s circulation theorem ⇒

Convergent flow in the troposphere ⇒ cyclone Divergent flow in the UTLS ⇒ anticyclone

courtesy of Yong Wang

Randel and Park, JGR, 2006:

GPH and MPV at 150 hPa AIRS H2O and O3 at 360 K

Asian summer monsoon anticyclone

≈nearly stationary disturbance of the

...this high pressure system in the upper troposphere extends well into the lower stratosphere up to about 20 km (or^{θ =}420 K)

Randel and Park, JGR, 2006

Park et al., JGR, 2007:

strongly isolated anticyclone between 12 and 20 km, (from ACE-FTP data)

Haynes and Shuckburgh, JGR, 2000:

weak and permeble NH STJ during summer (from the effective diffusivity concept)

Dethof at al., QJRMS, 1999:

Bannister at al., QJRMS, 2004:

Gettelman et al., JGR, 2004:

Levine et al., JGR, 2007:

James et al., GRL, 2008:

strong contribution to the moist phase of the tape-recorder

2-month (July and August) aver- age NCEP zonal wind (shaded) and temperature anomalies (thin lines, deviation from zon. mean)

Asian summer monsoon: Why we should care ?

Park et al., JGR, 2007

Asian summer monsoon: Why we should care ?

HCN at 13.5 km, JJA Randel et al., Science, 2010 ...the monsoon circulation provides an effective pathway for pollution from Asia, India, and Indonesia to enter the global stratosphere...

...mainly SO2, but also H2O

averaged between 0 and 100 E

Asian summer monsoon: Why should we care ?

...the most populated and po- luted area on Earth, more than half the world’s population

...the strongest influence of the Earth orography on the compo- sition of the atmosphere

courtesy of Yong Wang dominated by orographic insula-

tion of the Himalaya (Boos and Kuang, Nature, 2010)

Objectives

Impact of the Asian summer monsoon on the distribution of CO, HCN, SO2, H2O, O3, and aerosols in the Tropical Tropopause Layer (TTL), i.e. at the “gateway” into the stratosphere

In particular:

How important is the isentropic transport from the extratropics (from the northern summer hemisphere) into the TTL (in-mixing) ?

(e.g. Chen et al., 1995, Dunkerton et al., 1995, Hayens and Shuckburgh, 2005, JGR)

Winter

TTL

Upwelling

380 K 350 K 420 K

Summer

In−mixing

Tropopause

Modeling with CLaMS

CLaMS - Lagrangian Chemistry Transport Model with ≈ 10⁶ air parcels

air parcel = “pivotal point with mixing ratios µi, of m species with i = 1, ..., m”

Potential temperature/pressure as vertical coordinate in the stratosphere/troposphere Horizontal meteor. winds (ECMWF, NCEP, WACCM)

Vertical velocity: diabatic approach (θ˙ from radiation, latent heat rather than p)˙ Lagrangian mixing

Full stratospheric and

simplified tropospheric chemistry

Lagrangian particle sedimentation scheme parallelized code (JUMP)

McKenna et al., JGR, 2002, Konopka et al., JGR, 2004, Grooß et al., 2005, ACP, Konopka et al., 2007, 2010, ACP

Mixing Trajectory

Chemistry

Sedimentation

0000 00 1111 11 0000

00 1111 11 0000

00 1111 11 0000

00 1111 11

0000 00 1111 11

0000 00 1111 11

0000 00 1111 11 0000

00 1111 11

0000 00 1111 11

0000 00 1111 11 0000 00 1111 11

0000 00 1111 11

Euler versus Lagrange

Left: Casper David Friedrich: Wan- derer above the Sea of Fog

Bottom: Montgolfier ballon over Ro- camadour

Lagrangian view of transport

Mixing Chemistry

Advection

Chemistry Advection

driven by given wind fields

along the trajectories

Tracer

transport =

Advection

(Trajectories) (reversible)

+

Mixing

(Adaptive grid)

(irreversible)

Euler versus Lagrange

To solve: ∂tni + ∇ · (niu) = 0, niu = niu¯ + niu^′, niu^′ = D∇ni (Fick’s law)

ni - number densities of species i, i=0,...,m, u¯ - velocity of the flow, D - diffusion coefficient,

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 1

000000000000000000000000000 111111111111111111111111111

000000000000000000000000000 111111111111111111111111111

000000000000000000000000000 111111111111111111111111111

000000 000000 000000 000000

111111 111111 111111 111111

00000 00000 00000 00000 00000 00000 00000 00000

11111 11111 11111 11111 11111 11111 11111 11111

00000 00000 00000 00000 00000 11111 11111 11111 11111 11111

0000000 0000000 0000000 0000000 1111111 1111111 1111111 1111111

0000 0000 0000 0000 0000 00

1111 1111 1111 1111 1111 11

000000 000000 000000 000000 000000 000

111111 111111 111111 111111 111111 111

00000000 00000000 00000000 00000000

11111111 11111111 11111111 11111111

000000 000000 000000 000000 000000 000000 000000 000000

111111 111111 111111 111111 111111 111111 111111 111111

0000 0000 0000 0000

1111 1111 1111 1111

000000 000000 000000 000000 000

111111 111111 111111 111111 111

00000000 00000000 00000000 0000

11111111 11111111 11111111 1111

00000 00000 00000 00000 11111 11111 11111 11111

00000000 00000000 00000000 00000000

11111111 11111111 11111111 11111111

00000000 00000000 00000000 00000000

11111111 11111111 11111111 11111111

00000000 00000000 00000000 11111111 11111111 11111111

0000000 0000000 0000000 1111111 1111111 1111111

00 11

00 11

00 11

00 11

00 11

00 11 00

11 00 11

00 11

00 11

00 11 00 11

00 11

00 11

00 11 00

11

00 11

00 11 0000

0000 0000 0000

1111 1111 1111 1111

0000 1111

0000 0000 0000 0000 0000

1111 1111 1111 1111 1111

00000000 00000000 0000 11111111 11111111 1111000000000000000000

111111 111111

111111 00000000000000000000000000000000000000000000000000000000 11111111 11111111 11111111 11111111 11111111 11111111 11111111

000000 000000 000000 000000

111111 111111 111111 111111

00000000 00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 11111111 1111

000000 000000 000000 111111 111111 111111

Euler versus Lagrange

To solve: ∂tni + ∇ · (niu) = 0, niu = niu¯ + niu^′, niu^′ = D∇ni (Fick’s law)

ni - number densities of species i, i=0,...,m, u¯ - velocity of the flow, D - diffusion coefficient, Eulerian reference frame is a way of looking at

fluid motion that focuses on specific points in the space through which the fluid moves

(regular grid)

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 0000000000000000000000000000 1111111111111111111111111111

0000000000000000000000000000 1111111111111111111111111111

0000000000000000000000000000 1111111111111111111111111111

0000000000000000000000000000 1111111111111111111111111111

00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 1111

00000000 00000000 00000000 00000000

11111111 11111111 11111111 11111111

000000 000000 000000 000000 000000 111111 111111 111111 111111 111111

000000 000000 000000 000000 111111 111111 111111 111111

0000 0000 0000 0000 0000 00

1111 1111 1111 1111 1111 11

00000000 00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 11111111 1111

00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 1111

00000 00000 00000 00000 00000 00000 00000 00000

11111 11111 11111 11111 11111 11111 11111 11111

0000 0000 0000 0000 00

1111 1111 1111 1111 11

00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 1111

00000000 00000000 00000000 0000

11111111 11111111 11111111 1111

00000 00000 00000 00000 11111 11111 11111 11111

00000000 00000000 00000000 00000000

11111111 11111111 11111111 11111111

00000 00000 00000 00000 00000 00000 00000 00000

11111 11111 11111 11111 11111 11111 11111 11111

00000000 00000000 00000000 11111111 11111111 11111111

000000 000000 000000 111111 111111 111111

Physical mixing D “overloaded” by numerical diffusion ∼ ∆x²/∆t ≈ 10⁶m²/s ≫ D, for

∆x = 100 km, ∆t = 10 min (Courant criterion)

00 11

00 11

00 11

00 11

00 11

00 11 00

11 00 11

00 11

00 11

00 11 00 11

00 11

00 11

00 11 00

11

00 11

00 11 0000

0000 0000 0000

1111 1111 1111 1111

0000 1111

0000 0000 0000 0000 0000

1111 1111 1111 1111 1111

00000000 00000000 0000 11111111 11111111 1111000000000000000000

111111 111111

111111 00000000000000000000000000000000000000000000000000000000 11111111 11111111 11111111 11111111 11111111 11111111 11111111

000000 000000 000000 000000

111111 111111 111111 111111

00000000 00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 11111111 1111

000000 000000 000000 111111 111111 111111

Euler versus Lagrange

To solve: ∂tni + ∇ · (niu) = 0, niu = niu¯ + niu^′, niu^′ = D∇ni (Fick’s law)

ni - number densities of species i, i=0,...,m, u¯ - velocity of the flow, D - diffusion coefficient, Eulerian reference frame is a way of looking at

fluid motion that focuses on specific points in the space through which the fluid moves

(regular grid)

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 0000000000000000000000000000 1111111111111111111111111111

0000000000000000000000000000 1111111111111111111111111111

0000000000000000000000000000 1111111111111111111111111111

0000000000000000000000000000 1111111111111111111111111111

00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 1111

00000000 00000000 00000000 00000000

11111111 11111111 11111111 11111111

000000 000000 000000 000000 000000 111111 111111 111111 111111 111111

000000 000000 000000 000000 111111 111111 111111 111111

0000 0000 0000 0000 0000 00

1111 1111 1111 1111 1111 11

00000000 00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 11111111 1111

00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 1111

00000 00000 00000 00000 00000 00000 00000 00000

11111 11111 11111 11111 11111 11111 11111 11111

0000 0000 0000 0000 00

1111 1111 1111 1111 11

00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 1111

00000000 00000000 00000000 0000

11111111 11111111 11111111 1111

00000 00000 00000 00000 11111 11111 11111 11111

00000000 00000000 00000000 00000000

11111111 11111111 11111111 11111111

00000 00000 00000 00000 00000 00000 00000 00000

11111 11111 11111 11111 11111 11111 11111 11111

00000000 00000000 00000000 11111111 11111111 11111111

000000 000000 000000 111111 111111 111111

Physical mixing D “overloaded” by numerical diffusion ∼ ∆x²/∆t ≈ 10⁶m²/s ≫ D, for

∆x = 100 km, ∆t = 10 min (Courant criterion)

Lagrangian reference frame is a way of look- ing at fluid motion where the observer follows individual fluid particles as they move through space and time

(irregular grid)

00 11

00 11

00 11

00 11

00 11

00 11 00

11 00 11

00 11

00 11

00 11 00 11

00 11

00 11

00 11 00

11

00 11

00 11 000000

000000 000000 000000 000

111111 111111 111111 111111 111

0000 1111

000000 000000 000000 000000 000000

111111 111111 111111 111111 111111

00000 00000 00000 00000 00000 11111 11111 11111 11111 11111000000000000000000000

111111 111111 111111 111

0000000 0000000 0000000 0000000 0000000 0000000 0000000

1111111 1111111 1111111 1111111 1111111 1111111 1111111

0000 0000 0000 0000 00

1111 1111 1111 1111 11

000000 111111

00000000 00000000 00000000 00000000 00000000 0000

11111111 11111111 11111111 11111111 11111111 1111

00000 00000 00000 11111 11111 11111

r(t)

Mixing is under control. Advection means cal- culation of trajectories

dr(t)

...numerical diffusion versus

atmospheric mixing

Stratospheric stirring

...stratospheric transport is dom- inated by horizontal winds. Due to a strong stable stratification, the vertical motion is supressed.

...stratosphere looks like mixing colors with a stir- ring stick.

Euler versus Lagrange

t=t

t=t

t=t

t=t

1

2

3

4

u

Eulerian grid

...one of the most intriguing features offered by the La- grangian transport is the possibility to to parameterize the “true” physical mixing in terms of the numerical dif- fusion...

Grid adaptation ⇒ mixing

A C B

quasiuniform distribution of air parcels

Delaunay triangulation ⇒ next neighbors

Grid adaptation ⇒ mixing

A C B

quasiuniform distribution of air parcels

Delaunay triangulation ⇒ next neighbors

sheared flow

∆t = 6 − 24 hours

Grid adaptation ⇒ mixing

A C B

quasiuniform distribution of air parcels

Delaunay triangulation ⇒ next neighbors

sheared flow

∆t = 6− 24 hours

A C B

D

grid adaptation =

regridding of the deformed grid

⇒ new air parcels

⇒ interpolations (num. diffusion)

⇒ mixing

So, how to proceed ?

Two problems have to be solved:

To find an appropriate (irregular) Lagrangian grid (i.e. parameters ∆r and ∆z). The numerical diffusion due to the interpolations within such a grid can be estimated as

D^num_h ≈ ∆r²/∆t D_v^num ≈ ∆z²/∆t.

and, consequently:

D_h^num

D_v^num = ∆r²

∆z² = α² = Dh

Dv

, α = ∆r

∆z aspect ratio

Dv, D_h - ‘true” vertical and horizontal diffusivities in a horizontal and stably stratified flow (Haynes and Anglade, JGR, 1997).

So, how to proceed ?

...and the second problem is:

To find a (physical) mechanism how to trigger such interpolations. Here, we follow the idea of the gradient Richardson number:

Ri = N²

∂u

∂z

2

+

∂v

∂z

2 i.e. mixing occurs only for sufficiently small values of Ri < Ric

with u, v denoting the horizontal wind components and N the Brunt Vaisala frequency.

...i.e. mixing happens either when the wind shear is great enough to overpower any stabilizing buoyant forces (denominator is large), or when the dry or, more general, moist environment is static instabile (numerator is small or even negative).

1st step:

to choose the right grid...

(Konopka et al., Geophysical Monograph Series, 2012)

Entropy and static stability based grid

0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000 0000000000000000000

1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111 1111111111111111111

320 K 350 K

360 K

450 K

380 K 420 K

600 K

Tropopause

UTLS

TR ST

High Latitudes

TR UTLS ST

TR UTLS ST

Mid−Latitudes Tropics

Stratosphere (Overworld)

ST

TR

UTLS

S

S = = S

Vα > V < < V

α > α

<

<

“Same entropy per air parcel”

Sap = ∆r²∆z s(θ, ρ) = const, s(θ, ρ) = cpρln θ θ0

“Aspect ratio proportional to static stability”

α = ∆r

∆z ∼ N, N² = g θ

dθ

dz (Brunt Vaisala frequency)

Why entropy ?

0000000000000000 0000000000000000 0000000000000000 0000000000000000 0000000000000000 0000000000000000 0000000000000000 0000000000000000 0000000000000000

1111111111111111 1111111111111111 1111111111111111 1111111111111111 1111111111111111 1111111111111111 1111111111111111 1111111111111111 1111111111111111

Stratosphere

Troposphere Mesosphere

S T

T

∆

ref

ref S + Sref

adiabatic

∆ S

∆ S

∆ ^S

Carnot cycle

"same available work"

...in a system where no additional information is available, same entropy means that each air parcel contains the same amount of available energy that is transferable into work that manifests as atmospheric motion. Such motion may irreversibly dissipate into friction.

Definition of the grid

Thus:

nap = 1

∆r²∆z = s Sap

α = ∆r

∆z = kN nap - density of air parcels

α - aspect ratio

∆r =

kN Sap

s

¹₃

∆z =

1

kN

²₃

Sap

s

¹₃

N and s examplary de- rived from ERA-Interim for 1.01.2002.

Scaling properties

Vertical diffusivity Dv per mixing event ⇒

Vertical diffusivity Dv per volume unit ⇒

N and s examplary de- rived from ERA-Interim for 1.01.2002.

2st step:

to trigger mixing by

physical parameters...

Lyapunov exponent λ

r₀

t=t₀

Consider an air parcel sur- rounded by a small circle of ra- dius r0.

t=t + t r r

+

−

0

After a time ∆t and for sufficiently small values of r0, the circle is deformed into an ellipse with minor and major axes r⁻ and r+

Lyapunov exponent λ

r₀

t=t₀

Consider an air parcel sur- rounded by a small circle of ra- dius r0.

t=t + t r r

+

−

0

After a time ∆t and for sufficiently small values of r0, the circle is deformed into an ellipse with minor and major axes r⁻ and r+

Definition: (Lyapunov exponent)

λ^± = ± 1

∆t ln r^± r0

for sufficiently small ∆t and r0

Incompressible flows ⇒ (r₀² = r⁻r+) ⇒ λ⁻ = λ+

Dynamically adaptive grid

Before the advection step

A C B

Determine nearest neighbors (e.g. for point A), r0 - mean distance between air parcels

Set the critical Lyapunov exponent λc

and the time step ∆t (free parameter) Define r^c_±

r±^c = r0 exp±λc∆t

Dynamically adaptive grid

Before the advection step

A C B

Determine nearest neighbors (e.g. for point A), r0 - mean distance between air parcels

Set the critical Lyapunov exponent λc

and the time step ∆t (free parameter) Define r^c_±

r±^c = r0 exp±λc∆t

After the advection step

A C B

D

If r > r₊^c , then a new grid point D is inserted midway between A and B (insertion)

If r < r^c₋, then grid points A and C are removed and a new grid point is intro- duced midway between the positions of A and C (merging)

Mixing in CLaMS

Large-scale wind

Small-scale deformations

Filamentation

Mixing

(irreversibility)

Mixing in the vicinity of the subtropical jet

Subtropical jet

over Himalayas

Mixing in the vicinity of the subtropical jet

Subtropical jet over Himalayas

Strong

deformations ...

Mixing in the vicinity of the subtropical jet

Subtropical jet over Himalayas

... and mixing !

Pan et al., 2006, JGR

λ _c - “critical Lagran-

-gian deformation”

A completely different view...

...regular (Euler)

A completely different view...

...regular (Euler)

versus irregular (Lagrange)

courtesy of Rolf Müller

...and chemistry

species lower boundary upper boundary

CH4 CMDL HALOE

Mean Age linear source MIPAS (SF6)

CO2 CMDL Mean Age

CO CMDL + MOPITT Mainz-2D

O3 0 HALOE, θ ≥ 500 K

O3 (tracer) 0 HALOE, θ ≥ 500 K

HCl 0 HALOE, θ ≥ 500 K

H2O ECMWF, θ ≤ 280 K HALOE

N2O, F11 CMDL (CATS) 0

HCN MODIS 0

Simplified chemistry

CH4 ⇒ (OH, O(¹D), Cl) ⇒ H2O, CO ⇒ (OH) ⇒ CO2

(hν) ⇒ O3 ⇒ (HO_x) ⇒, N2O, F11 ⇒ (O(¹D), hν) ⇒ HCN ⇒ (OH, O(³D), uptake by the ocean)⇒

Multi-annual CLaMS simulations (2001-10)

- HALOE - Climatology:

Grooss and Russell, ACP, 2005 - CMDL: GLOBALVIEW, 2007 CO2/CH4/CO since 1979/84/91 P. Tans, K. Masarie, P. Novelli - CMDL: CATS (4 stations) N2O, F11, J. Elkins

- MIPAS, SF6-Age Stiller et al., ACP, 2008 - MOPITT (V3, V4)

Pommrich at al., PhD, 2008 - HCN

Pommrich at al., GRL, 2010

...isentropic thinking

diabatic rather than kinematic vert. velocities

potential temperature θ defines the vertical coordinate

Cross isentropic velocity θ˙ derived from diabatic processes (long- and shortwave radiation with clouds + laten heat +,...),

⇒ σ-θ, hybride ζ-coordinate (Mahowald et al., JGR, 2002)

diabatic rather than kinematic vert. velocities

potential temperature θ defines the vertical coordinate

Cross isentropic velocity θ˙ derived from diabatic processes (long- and shortwave radiation with clouds + laten heat +,...),

⇒ σ-θ, hybride ζ-coordinate (Mahowald et al., JGR, 2002)

p [hPa]

340 360 380

310

280 100

200

300

500

1013

[K]

0.12

0.25

0.80 0.40

1.00

θ ^=p/p

10 30 50 70

[deg N]

Subtropical Jet σ

ζ = θ (pot. Temp.) above 300 hPa

dζ

dt = ^dθ_dt

diabatic rather than kinematic vert. velocities

potential temperature θ defines the vertical coordinate

Cross isentropic velocity θ˙ derived from diabatic processes (long- and shortwave radiation with clouds + laten heat +,...),

⇒ σ-θ, hybride ζ-coordinate (Mahowald et al., JGR, 2002)

p [hPa]

340 360 380

310

280 100

200

300

500

1013

[K]

0.12

0.25

0.80 0.40

1.00

θ ^=p/p

10 30 50 70

[deg N]

Subtropical Jet σ

ζ = θ (pot. Temp.) above 300 hPa

dζ

dt = ^dθ_dt

ζ ∼ σ = p/ps, p - surf. pressure below 300 hPa

dζ = ˙σ