Using Data Assimilation to Explore Precipitation - Cloud System -
Environment InteractionsDerek J. Posselt
Collaborators:Samantha Tushaus, Richard Rotunno, Marcello Miglietta,
Craig Bishop, Marcus van Lier-Walqui, Tomislava Vukicivic
Sponsors:NASA Modeling, Analysis and Prediction
National Science FoundationOffice of Naval Research
Cloud System - Environment Interaction
D. J. Posselt 2
Posselt et al., 2012 (J. Climate)
• 3D Wind profile• Land surface properties• Thermodynamic environment• Cloud microphysics• Aerosol content and chemistry
• Cold pools• Updraft/downdraft strength• Latent heat release• Vertical condensate distribution• Radiative fluxes and heating rates• Precipitation rate and amount
OutcomesControls
Data Assimilation:Quantifying Relationships
The model represents the relationship between controls on, and output from, a system (e.g., cloud resolving model)
Can assess sensitivity of output to changes in input
D. J. Posselt 3
All Possible Input Model All Possible Output
Can also ask which sets of inputs could have produced a given set of outputs
Uncertainties represented as probabilities
F(x)
P(x)P(y)
P(x|y)
P(y|x)
Quantifying Response: Brute ForceGoal: estimate P(y|x) and/or P(x|y)Options: Discretize P(y|x) and P(x)
and compute P(x|y) Specify a range of parameter values Run the model repeatedly in small
increments of the control parameters
Thorough, but very computationally expensive
D. J. Posselt 4
Sensitivity Analysis via Monte CarloGoal: estimate P(y|x) and/or P(x|y)Options: Randomly sample P(x|y)
(traditional Monte Carlo, latin hypercube) Evaluate P(y|x) and P(x)
at points randomly distributed in parameter space
Compute sample of P(x|y) Fill the response surface using
Kernel density estimate Interpolation Function fitting
D. J. Posselt 5
Cloud Sensitivity Analysis via Bayesian Sampling
Goal: estimate P(y|x) and/or P(x|y)Options: Construct a Markov chain
that samples P(x|y) A random walk guided by
information from observations
D. J. Posselt 6
Markov chain Monte Carlo: Avoids states that provide a poor fit
to observations Flexible probability distributions
Posselt and Vukicevic (2010, Mon. Wea. Rev.), Posselt and Bishop (2012, Mon. Wea. Rev.), van Lier-Walqui et al. (2012, 2013 Mon. Wea. Rev.), Posselt, Hodyss, and Bishop (2014, Mon. Wea. Rev.)
Two Experiments1. Convection – Microphysics Interaction Sensitivity of convective cloud properties to changes in
cloud microphysical parameters Cloud microphysics – dynamics – thermodynamics
interaction2. Multivariate Sensitivity of Orographic Rainfall Sensitivity of mountain rainfall to changes in mountain
geometry and upwind sounding Which combinations of geometry and sounding produce
heavy upslope precipitation?
D. J. Posselt 7
Two Experiments1. Convection – Microphysics Interaction Sensitivity of convective cloud properties to changes in
cloud microphysical parameters Cloud microphysics – dynamics – thermodynamics
interaction2. Multivariate Sensitivity of Orographic Rainfall Sensitivity of mountain rainfall to changes in mountain
geometry and upwind sounding Which combinations of geometry and sounding produce
heavy upslope precipitation?
D. J. Posselt 8
1. Convection – Microphysics Interaction:
D. J. Posselt 9
64 km (x), 24 km (y), 72 levels, dx=2km1 x 106 simulations
Three phases: Developing: 180-230 minutes Mature: 230-280 minutes Dissipating: 280-330 minutes
Perturb cloud microphysics Characterize parameter sensitivity Observe bulk hydrologic cycle and
radiative flux – constrain simulation properties
Store ancillary data on dynamics, thermodynamic environment, and radiation – analyze relationships
Parameters and Observations
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10 Microphysics Parameters
Snow fall speed coefficient (as)
Snow fall speed exponent (bs)
Graupel fall speed coefficient (ag)
Graupel fall speed exponent (bg)
cloud-rain autoconversion (qc0)
Slope intercept Rain (N0r)
Slope intercept Snow (N0s)
Slope intercept Graupel (N0g)
Snow particle density (ρs)
Graupel particle density (ρg)
5 Observations Obs σ
Precipitation Rate 2 mm hr-1
Liquid Water Path (LWP) 0.5 kg m-2
Ice Water Path (IWP) 1.0 kg m-2
Longwave Flux (OLR) 5 W m-2
Shortwave Flux (OSR) 5 W m-2
Obs taken in 3 time intervals• Developing (180-230 min)• Mature (230-280 min)• Dissipating (280-330 min)
Defined according to cloud depthand surface rain rate
Ice
Fall
Spe
eds
War
mR
ain
Ice
PS
DIc
e D
ensi
ty
Parameter Sensitivity:Posterior Parameter PDFs P(x|y)
Given a set of outcomes (Pcp, LWP, IWP, OLR, OSR) Which sets of parameters could have produced them? Questions: What is the response of model output to changes in cloud
microphysical assumptions? P(y|x) How do changes in parameters affect convective structure? P(z|x)
D. J. Posselt 11
Warm RainGraupel
Fall SpeedSnow
Fall SpeedSnow
DensityGraupel Density Ice PSD
Hydrologic Cycle / Radiative Flux Response
Forward observations vs parameters
D. J. Posselt 12
Dev
elop
ing
Mat
ure
Dis
sipa
ting
Pre
cip
Rat
e
LWP
IWP
OLR
OS
R
N0r N0r N0r qc0 qc0
Pre
cip
Rat
e
LWP
IWP
OLR
OS
R
Pre
cip
Rat
e
LWP
IWP
OLR
OS
R
N0r N0r ag qc0 qc0
ag ag agρg ρg
Warm rain controls thesolution early
Warm rain and ice processesimportant at maturity
Ice processescontrol thesolutionlate
Storm-Scale Dynamic – Thermodynamic interactions
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Bimodal solution: Weaker up/downdrafts, near-zero LHR, dry, warm Stronger up/downdrafts, negative LHR, moist, cool
Mature Phase Low Level W+
Mature Phase Low Level W-
Dissipating Phase Low Level LHR
Dissipating Phase Low Level RH
Dissipating Phase Low Level Tclear
DowndraftUpdraft Latent Heat Release Relative Humidity Clear Air TemperatureP
roba
bilit
y
Pro
babi
lity
Pro
babi
lity
Pro
babi
lity
Pro
babi
lity
Microphysics – Latent Heating
Low level latent heating profiles sensitive to warm rain parameters at all times.Note different solutions associated with cold pools.
D. J. Posselt 14
Late
nt H
eat R
elea
se
N0r
Late
nt H
eat R
elea
se
N0r N0r
Developing Phase, Low Level Mature Phase, Low Level Dissipating Phase, Low Level
Late
nt H
eat R
elea
se
Late
nt H
eat R
elea
se
Late
nt H
eat R
elea
se
Late
nt H
eat R
elea
se
qc0 qc0 qc0
Developing Phase, Low Level Mature Phase, Low Level Dissipating Phase, Low Level
Two Experiments1. Convection – Microphysics Interaction Sensitivity of convective cloud properties to changes in
cloud microphysical parameters Cloud microphysics – dynamics – thermodynamics
interaction2. Multivariate Sensitivity of Orographic Rainfall Sensitivity of mountain rainfall to changes in mountain
geometry and upwind sounding Which combinations of geometry and sounding produce
heavy upslope precipitation?
D. J. Posselt 15
Two Experiments1. Convection – Microphysics Interaction Sensitivity of convective cloud properties to changes in
cloud microphysical parameters Cloud microphysics – dynamics – thermodynamics
interaction2. Multivariate Sensitivity of Orographic Rainfall Sensitivity of mountain rainfall to changes in mountain
geometry and upwind sounding Which combinations of geometry and sounding produce
heavy upslope precipitation?
D. J. Posselt 16
2. Orographic Precipitation(S. Tushaus, Poster 1080)
CM1 model, stable upslope rainfall 2D (x-z) 800 km long, dx = 2 km, 59
levels Analytical moist-stable sounding,
Gaussian bell mountain, warm rain microphysics
Observe precipitation in 6 regions
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6 Environment ParametersWind speed (U)Moist Brunt Vaisala Freq (Nm
2)Surface potential temperature (Ts)Relative Humidity (RH)Mountain heightMountain half-width
Parameter Sensitivity Examine functional response of precipitation Explore joint parameter PDFs
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Pre
cipi
tatio
n (m
m/h
r)
Mtn Ht (m) Mtn Width (m) Wind (m/s) RH Nm2 (s-2) Tsfc (K)
Upslope Precipitation Response to Change in Parameters
Parameter Sensitivity Tipping point in Ts
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Interaction between Ts and stability Back-propagating mountain wave Strong precipitation response to a small change in profile
…examine change in structure
Multivariate Precipitation Response How does sensitivity change with parameter value?
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Changetwo parameters
at a time
Changeall parameterssimultaneously
Summary: MCMC-based Bayesian sensitivity experiments identify key
microphysical parameters and their relationship to dynamics and environment
Joint PDF of parameters with model states lends information on cloud-environment interaction1. There are multiple stable states in each system; different
combinations of parameters produce similar integral observations in very different dynamic and thermodynamic environments
2. Convective cold pools responsive to changes in PSD parameters, but with two distinct preferred states
3. Tipping point in orographic precipitation system: rapid change in outcome for a small change in input
4. Strong changes in sensitivity in multivariate orographic case
D. J. Posselt 21
Next Steps Composite analysis of large ensembles
of model states – processes Extension to other dynamical systems Tropical and extratropical cyclones (in progress) Cloud-aerosol interaction (in progress)
Examination of observation information content Dual-polarization radar Combined cloud radar – microwave retrievals
D. J. Posselt 22
van Lier-Walqui et al. (2012, 2014, MWR) Posselt, Hodyss, and Bishop (2014, MWR) Posselt and Mace (2014, JAMC)
References: Posselt and Vukicevic (2010, MWR) Posselt and Bishop (2012, MWR)
PDF Sampling: Markov Chain Monte Carlo
D. J. Posselt 23
Parameter 1
Par
amet
er 2
Storm-Scale Dynamics Column integral
constraint on microphysical parameters leads to constraint on storm scale dynamics
Long tail toward stronger storms (stronger updrafts and downdrafts)
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Mid-level, Mature Mid-level, Dissipating
Mid-level, Mature Mid-level, DissipatingUpdraft Updraft
Downdraft Downdraft
Pro
babi
lity
Pro
babi
lity
Pro
babi
lity
Pro
babi
lity
PSD – Cold Pool Relationships
Rain particle size distribution influence on low-level downdrafts at maturity and on cold pools at dissipation
D. J. Posselt 25
Dow
ndra
ft
N0r
Rel
ativ
e H
umid
ity
N0r
T (c
lear
)
N0r
Mature Phase, Low Level Dissipating Phase, Low Level Dissipating Phase, Low Level
3D Control Simulation, w and cloud
Three Phases: Developing:
180-230 minutes Mature:
230-280 minutes Dissipating:
280-330 minutesModel Configuration: 64 x 24 km domain 2 km dx, dy 72 vertical levels
D. J. Posselt 26
3D Control Simulation, w and cloud
Three Phases: Developing:
180-230 minutes Mature:
230-280 minutes Dissipating:
280-330 minutesModel Configuration: 64 x 24 km domain 2 km dx, dy 72 vertical levels
D. J. Posselt 27
3D Control Simulation, w and cloud
Three Phases: Developing:
180-230 minutes Mature:
230-280 minutes Dissipating:
280-330 minutesModel Configuration: 64 x 24 km domain 2 km dx, dy 72 vertical levels
D. J. Posselt 28