Mesoconvective organization

1
Meso-convective organization
Mitchell W. Moncrieff Cloud Systems Group NCAR
Pacific Institute for the Mathematical Sciences,
University of Victoria, Victoria, BC, July 31
Aug 3 2007
2
Meso-convective organization

• Cumulus fields interacting mutually, with waves,
  and with the mean state generating coherent
  structures of spatio-temporal scale gtgt scale of
  individual cumulus
• Intrinsically a systemic upscale property,
  convective organization (conceptually) resembles
  coherent structures in turbulent fluids
• Macrophysics of cloud systems especially latent
  heating and evaporative cooling of
  precipitation interacting with shear is key to
  propagating systems
• Much known about the convective organization
  process, less about its role in the large-scale
  atmospheric circulation
• Parameterization of convective organization
  differs fundamentally from the parameterization
  of cumulus dynamics
• Cloud-system resolving models (CRM) quantify
  large-scale role of convective organization

3
Precipitating convective systems a problem of
control and feedback
4
Meso-convective organization is i) not
represented in convective parameterizations used
in contemporary global models ii) exists in
global CRMs (explicit convection)iii) exists
in superparmeterized global models (explicit
convection) i) an intellectual challenge
ii) and iii) key questions are to what degree
are these realizations realistic if not, why not
?
5
Comment on resolution

• Physical resolution of a numerical model is
• where 7 lt N lt 10 and the grid-spacing
• Therefore, physical resolution is about an order
  of magnitude coarser than the grid spacing
• Resolving cumulonimbus requires 100 m
• CRMs ( 3 km) are truncated where growth
  rates, scale interaction and energy exchange are
  maximal may distort feedback and scale
  interaction challenge for global CRMs
• Aspect ratio of mesoscale circulations is 10
  therefore, CRMs represent convective organization
  explicitly quantifying its global role

6
CRM grids
Amplitude of vertical kinetic energy
No plausible scale-gap
Scale gap
Resolved scales
1km grid
10 km grid
Horizontal scale
Strong inter-scale exchange of moist energy
7
Convective organization beyond contemporary
parameterization
Implicit cumulus parameterization
Explicit mesoscale dynamics
8
CAPE, shear and convective regimes
Strong CAPE
Moderate CAPE
Weak CAPE
Weak shear
Moderate shear
Strong shear
Grabowski et al (1998)
9
Squall line
10
(No Transcript)
11
African mesoscale convective systems
12
Continental propagating convective systems and
mountainous terrain
Satellite-derived brightness temperature - Laing
and Fritsch (1997)
13
Diurnal variability of summer precipitation
Knievel et al. (2004)
14
Diurnal variability and timing of summer
precipitation over the continental U.S.
Knievel et al. (2004)
15
Convective organization MJO/Kelvin regime
16
Convective organization non-MJO regime
17
MJO Hierarchical convective organization
Super- clusters
Mesoscale convective systems
MJO envelope
Cumulonimbus (not resolved in this satellite
image)
Nakazawa (1988)
18
Elementary concepts
19
Convective overturning CAPE
z
Final
Initial
g
Initial PE
Final PE
Change of PE Convective Available Potential
Energy, CAPE
For each parcel provided
20
CAPE

• Initiation of convection usually requires
  finite-amplitude boundary layer lifting to
  release CAPE
• Kinetic energy of forced ascent must exceed the
  convective inhibition (CIN)

Convective Inhibition (CIN)
21
Thermodynamic vs dynamic lifting

• Convective parameterizations usually triggered
  using simple thermodynamic concepts warm bubble
  lifted to test for a level of free convection
• Involves the diurnal evolution of convection
• Organized convection downdraft outflow (density
  currents) and convectively generated gravity
  waves cause non-local dynamic lifting

Free atmosphere
Level of free convection (LFC)
Lifted test parcel
Boundary layer
22
Downdrafts trigger cumulus
Lifting at nose of density current triggers new
convection
Cold downdraft (density current)
C
23
CRM-simulated precipitation and downdrafts
(density currents) no shear
24
Early conceptual model severe hailstorm
Browning and Ludlam (1963)
25
Forms of energy associated with meso-convective
organization

• Kinetic energy of updrafts and downdrafts
  supplied by CAPE, kinetic energy, pressure work
• Downdrafts generate cold pools (density
  currents)
• Propagation speeds of cloud system (C) and
  density currents (C1, C2) are equal only in
  special circumstances
• Key environmental shear

C
CAPE
Dynamics
cold pool
C2
C1
26
b) Tropical squall line (propagating regime)
Conceptual models of organized convection
a) Midlatitude severe storms (steering-level
regime)
Occurs in jet-like wind profiles (reverse shear)
Browning and Ludlam
27
Approach Lagrangian dynamics of steady organized
convection in shear
28
First integral of the mass, momentum, moist
thermodynamics and energy equations
29
Fundamental first integral
What are the F - functions ?
30
Lagrangian integrals

• Fundamental Theorem of Calculus

31
2-D vorticity
32
Thermodynamics
33
Energy
34
Eulerian momentum constraint
35
Integro-differential equation
36
Framework for

• Dynamically self-similar motion systems
• - density currents
• - frontal rainbands
• - propagating convective systems

37
Simplest paradigm
38
Organization by shear

• CAPE normalized by kinetic energy convective
  Richardson number

z
U
39
Inaugural model
a)

• Far-field solution to the integro-differential
  equation for constant shear (A)

b)

40
Free boundary problem

• Free-boundary
• Material surface ( )
• Pressure continuous

Far-field solution integro-differental equation
Far-field solution integro-differental equation
41
Whoops! Vertical tilt is
inconsistent with the 2D conceptual model
42
Momentum transport
43
Steering-level regime does exist in nature 3D
transient convection
and 3D severe tornadic hailstorms
44
Dynamics missing from the 2-branch
model?Dynamics of meso-convective downdrafts
Formally, hydraulic work-energy principle
involving cross-system convectively-generated
pressure gradient
45
Analog model has 3 branches, not 2Extra branch
propagating (hydraulic jump) behaviorcharacter
the work-enerfgy principle
46
2) Propagating
Two regimes
1) Steering-level
Thorpe, Miller Moncrieff (1982), Moncrieff (1992)
Browning and Ludlam (1966)
Moncrieff Miller (1976)
Ludlam (circa 60s 1980)
47
2) Propagating regime
1) Steering-level regime
Thorpe, Miller Moncrieff (1982), Moncrieff (1992)
Browning and Ludlam (1966)
Moncrieff Miller (1976)
48
(No Transcript)
49
Weakly 3D MCS
50
Organization by shear

• CAPE normalized by kinetic energy convective
  Richardson number

z
U
51
Work-energy principle

• Work done by pressure normalized
  by inflow kinetic energy

C
52
2 dimensionless quantities and 3 forms of energy
(per unit mass) convective available potential
energy, kinetic energy and work done by pressure
gradient are fundamental to meso-convective
organization
53
Integro-differential equation
54
Free-boundary solution
55
Archetypal 2-D flow organization
Free-boundary solution
Regimes of organization a function of
56
Momentum transport and upshear tilt
z
-
Eddies tilt backward relative to propagation
vector
C
-

57
Realizable 2D flow regimes
58
3-branch regime in a 2D CRM single system
59
Squall line simulation
60
(No Transcript)
61
Comparison of analytic model with numerical
simulation
62
3-branch regime in a 2D CRM Multi-scale family
of cumulonimbus
63
W. African squall line upscale evolution of
cumulus
c
Lafore Moncrieff (1987)
64
3-branch regime in a 2D CRM Fully multiscale
systems
65
Key points

• Cloud-system resolving models (CRM) not eliminate
  convective parameterization, but change the
  formulation of the problem and the thought
  processes involved in its solution
• CRMs bring meso-convective organization to the
  fore and introduce dynamical aspects into
  parameterization
• CRMs change the character of the parameterization
  problem rather than obviate it

66
3-branch regime in a 2D CRM
Grabowski and Moncrieff (2001)
67
Precipitating systems generate the shear 1
m/s/day they require Dynamical feedback

• Shear
• generation
• Momentum
• transport
• Precipitation

10, 000 km
68
Strictly 2D MCS models
69
Momentum transport by squall lines

• Sign of momentum transport opposite to
  propagation vector
• Counter-gradient transport down-gradient
  momentum transport occur in different layers

Direction of propagation
70
Computational domain (600 km x 600 km x 40 km)
71
Regime of convective organization changes as the
environmental shear and forcing varies
72
Dynamical Lifting Mass Convergence

• Analytic model of airflow in an idealized
  convergence line (Liu and Moncrieff 1996)
• Mean vertical mass flux

73
Parameterization of Triggering

• Parameterization of triggering is based on
  dynamic considerations
• Relationships among the bulk thermodynamic
  quantities CAPE, DCAPE and CIN and the dynamical
  quantities UR, UL (and S) required
• CAPE and CIN defined by usual parcel lifting
  methods
• Specify hD and DCAPE µCAPE
• Convection theory gives S2URH
• Density current theory gives UR FD DCAPE
  1/2 where FD is a Froude number

74
Density current in shear

• R 0 (CAPE 0) yields analytic forms
  dependant on the Bernoulli number

Depth of downdraught
propagating system
Height of steering-level
75
Field-theory context for steering-level regime
76
Is (a) a dynamically correct 2D- solution and,
if not, why?
77
Key difference between (a) (b)
78
Archetypal dynamical model

• Limit case R 0 (CAPE 0) yields analytic
  forms that verify against observations
• Flow organization and propagation depend
  on

Depth of downdraught
propagating system
Height of steering-level
Moncrieff (1992)
79
Wave interpretation superposed n1, n2
circulations
Convective component
Phase Lag
Stratiform component
80
Westward-moving cluster embedded n 1 2 wave
modes
MCS-like circulation
81
Squall systems in CRM
Grabowski and Moncrieff (2001)
82
Momentum flux and shear generation

• Top flow perturbation by organized convection
• Middle momentum flux in the 20,000 km domain,
  and mean flux
• Bottom precipitation

The simulated mesoscale systems generate the
shear flow they require to exist a positive
dynamical feedback
83
Simulated multiscale organization
Westward travelling squall systems
Eastward-traveling Kelvin-wave-like envelopes of
convection
Grabowski and Moncrieff (2001,2002)
84
Dynamical analogy between density currents and
squall lines
85
Dynamical analogy between density currents and
squall lines
86
CRM-simulated precipitation and downdrafts
(density currents) no shear
Liu and Moncrieff (2003)
87
Downdraft fronts trigger cumulus
Lifting at nose of density current triggers new
convection
Cold downdraft (density current)
C
88
Upshear downshear regimes distinct dynamic
lifting (triggering)

• Downshear outflow Erect updraft - anchors
  incipient convection to the trigger
• W (xR - xL) (UR UL)z - ½(SL SR)z2
  shear decreases W.
• Upshear outflow Tilted updraft - shallow
  lifting - incipient convection moves away from
  the trigger.
• W (xR - xL) (UR UL)z ½(SL SR)z2
  shear increases W.

89
No shear
Shear
90
(No Transcript)
91
(No Transcript)
92
(No Transcript)
93
Cold-frontal rainbands
94
Multiscale organization and large-scale tropical
waves
95
Hierarchical convective organization
Super- clusters
Mesoscale convective systems
MJO envelope
Cumulonimbus (not resolved in this satellite
image)
Nakazawa (1988)
96
Some similar propagation/structural issues occur
for clusters/superclusters in the MJO
Moncrieff and Klinker (1997)
97
Nonlinear phenomenological model of the MJO
Moncrieff (2004)
98
Multi-scale cloud-resolving simulation in NWP
data assimilation and the MJO
99
On Friday will talk about

• parameterizing meso-convective organization

100
Summary

• Cumulus fields interacting mutually, with waves
  and with the mean state, generating coherent
  structures of spatio-temporal scale gtgt scale of
  individual cumulus
• Intrinsically a systemic upscale property,
  convective organization (conceptually) resembles
  coherent structures in turbulent fluids
• Macrophysics of cloud systems especially latent
  heating and evaporative cooling of
  precipitation interacting with shear is key to
  propagating systems
• Much known about the convective organization
  process, less about its role in the large-scale
  atmospheric circulation
• Parameterization of convective organization
  differs fundamentally from the parameterization
  of cumulus dynamics to the fore
• Cloud-system resolving models (CRM quantify the
  large-scale role of convective organization