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

D. J. Posselt 10

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

D. J. Posselt 13

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

D. J. Posselt 17

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

D. J. Posselt 18

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

D. J. Posselt 19

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?

D. J. Posselt 20

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)

D. J. Posselt 24

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