microwave observations in the presence of cloud and ...cloud screening use clear-sky...

Microwave observations in the presence of cloud and precipitation

Alan Geer

Thanks to: Bill Bell, Peter Bauer, Fabrizio Baordo, Niels Bormann

ECMWF/EUMETSAT satellite course 2015: Microwave 2 Slide 1

Overview

Clear-sky microwave (yesterday)

- The microwave spectrum

- Microwave instruments

- Imager channels and the surface

- Temperature sounding channels

- AMSU-A channel 5 at ECMWF

All-sky microwave (today)

- Interaction of particles with microwave radiation

- Solving the scattering radiative transfer equation

- Cloud screening for clear-sky assimilation

- All-sky assimilation

ECMWF/EUMETSAT satellite course 2015: Microwave 2 2

Size parameter

Atmospheric particles and microwave radiation

30 GHz frequency ↔ 10mm wavelength (λ)


Particle type Size range, r Size parameter, x Scatteringsolution

Cloud droplets 5 – 50 μm 0.003 – 0.03 Rayleigh

Drizzle ~100 μm 0.06 Rayleigh

Rain drop 0.1 – 3 mm 0.06 – 1.8 Mie

Ice crystals 10 – 100 μm 0.006 – 0.06 Rayleigh, DDA

Snow 1 – 10 mm 0.6 – 6 Mie, DDA

Hailstone ~10 mm 6 Mie, DDA

rx

2

Spherical particles interacting with radiation

Negligible scattering (x < 0.002):

- at low microwave frequencies, liquid water cloud acts like a gaseous absorber

Rayleigh scattering (0.002 < x < 0.2):

- an approximate solution for spherical particles much smaller than the wavelength

Mie scattering (0.2 < x < 2000):

- a complete solution for the interaction of a plane wave with a dielectric sphere

- valid for all x, but depends on a series expansion in Legendre polynomials - can be slow to compute

Geometric optics (x > 2000):

- e.g. the rainbow solution for visible light


Discrete dipole approximation (DDA):

Other solution methods exist, e.g. T-matrix

Non-spherical particles interacting with radiation


1. Create a 3D model of a snow or ice particle

2. Discretise into many small polarisable points (dipoles). Grid spacing << wavelength

3. Solve computationally – can be slow

Scattering properties – single particles

Scattering cross-section: [m2]

- the amount of scattering as an equivalent “area”

Absorption cross-section: [m2]

- particles can absorb as well as scatter radiation

Scattering phase function:

- the amount of scattering in a particular direction (expressed in polar coordinates)


s

a

),( P

Sum or average over:

- Different orientations (or, in some ice clouds, a preferred orientation)

- Size distribution

- Particle habits: snow and ice shapes, graupel, cloud drops, rain etc.

Extinction coefficient [1/km] :

Single scatter albedo:

- Ratio of scattering to extinction

Asymmetry parameter – the average scattering direction

- g = 1 → completely forward scattering (~ not scattered at all)

- g = 0 → as much forward as back scattering (not necessarily isotropic)

- g = -1 → complete back-scattering (physically unlikely)

Scattering properties - bulk


sae

sa

ss

H() - radiative transfer model


Sensor Given p,T, q, cloud and precipitation on each atmospheric level, we can compute:

• τ - Layer optical depth

(absorption and scattering)

• ωs - Single scattering albedo

• - Scattering phase function

(usually represented only by g, the asymmetry parameter)

= direction vector in solid angle

Now just solve the equation of radiativetransfer (discretized on the vertical grid):

4

''ˆ)'ˆ,ˆ(4

1ˆˆ

dIPBId

dI ss

)'ˆ,ˆ( P

This can be complex to solve:

- , the radiance in one direction, depends on radiance from all other directions:

- and all levels depend on each other

But in non-scattering atmospheres (no cloud and precipitation) it’s easier:

- ωs = 0 , so

- we can do each layer sequentially


Radiative transfer solversScattering phase function

4

''ˆ)'ˆ,ˆ(4

1ˆˆ

dIPBId

dI ss

BId

dI

ˆˆ

I

'I

Scattering solvers

Reverse Monte-Carlo

- Great for understanding and visualisation

- An easy way to do 3D radiative transfer

- Much too slow for operational use: many thousands of “photons” are required for convergence to a useful level of accuracy

Accurate but too slow for use in assimilation:

- DISORT (Discrete ordinates) – a generalisation of the two-stream approach

- Adding / doubling, SOI (Successive Orders of Interaction)

Two-stream and delta-Eddington approaches

- What we use operationally at ECMWF (in RTTOV-SCATT)

- Though quite crude methods, the accuracy is usually more than sufficient: the main R/T error sources in NWP are rarely in the solver



Single scatteralbedo

Rain and snow flux [g m2 s-1]Cloud mixing ratio [0.1 g kg-1]

Extinction coefficient βe

[km-1]

Asymmetry

Snow

Rain

Water cloud

Altitude [km]

Cloud and precipitation at 91 GHzStrong scattering in deep convection

Cloud and precipitation at 91 GHzStrong scattering in deep convection


Rain

Sn

ow

Clo

ud

SSA [0-1]

No. of emissions

To sensor

[km]

[km

]

Cloud screening

Use clear-sky radiative transfer but remove situations where the observations are cloudy or precipitating

Cloud screening methods:

- FG departures in a window channel

- Simple LWP or cloud retrieval

Sounders: Grody et al. (2001, JGR)

Imagers: Karstens et al. (1994, Met. Atmos. Phys.)

Imagers: 37 GHz polarisation difference, Petty and Katsaros

(1990, J. App. Met.)

- Scattering index (SI)

Over land, or in sounding channels affected by ice/snow

scattering, not cloud absorption: Grody (1991, JGR)


AMSU-A channel 3 departures for cloud screening50.3 GHz observation minus clear-sky first guess (bias corrected), ocean surfaces


K

Cloud shows up as a warm emitter over a radiatively cold ocean surface

AMSU-A channel 3 departures for cloud screening50.3 GHz observation minus clear-sky first guess, ocean surfaces


FG departure [K]

3K limit

Warm tail = cloud

20% of observations removed

AMSU-A channel 3 departures for cloud screening50.3 GHz observation minus clear-sky first guess (bias corrected), ocean surfaces


K

AMSU-A channel 4 departures for cloud screening52.8 GHz observation minus clear-sky first guess (bias corrected), land surfaces < 500m; sea-ice


K

Ice and snow hydrometeors show up as cold scatterers over a radiatively warm land or ice surface

AMSU-A channel 4 departures for cloud screening52.8 GHz observation minus clear-sky first guess, land surfaces < 500m


FG departure [K]

0.7K limit

Poor surface emissivity

Cloud or poor surface emissivity

35% of observations removed

An approximate radiative transfer equation for window channels (no scattering)


ASA TTTT )1()1(1

,ST

AT)1(

Surface temperature, emissivity

AT)1(

Upwelling atmospheric contribution

Downwelling atmospheric contribution

ST

Observed brightness temperature

AT)1(1 Reflected downwelling radiation

Surface emission

Atmospheric transmittance

LWP and cloud retrievals

Simplify further by assuming surface and effective atmospheric temperature are identical

An even more approximate radiative transfer equation for microwave imager channels:


)1(1 20 TT

Observed TB at frequency ν

Surface emissivityAtmospheric

transmittance

Effective atmospheric and surface temperature

Polarisation difference

Observe v and h polarisations separately:

Compute the difference in brightness temperature


)1(1 20 VV TT

)1(1 20 HH TT

HVHV TTT 20

Polarisation difference at 37 GHz (SSMIS)


37v

[K]

37h

[K]

37v -37h

[K]

Approximate cloud and precipitation retrievals

Polarisation difference, e.g. 37v – 37h

- 40K threshold typically used to indicate precipitation

- Petty and Katsaros (1990, J. App. Met.)

Simple LWP retrieval:

-

- Imagers: Karstens et al. (1994, Met. Atmos. Phys.)

- Sounders (additional zenith angle dependence): Grody et al. (2001, JGR)

- Homework for the keen – derive this by assuming:

(where k=mass absorption coefficient [m-1 (kg m-3) -1]; θ=zenith angle, LWP, TCWV are

column integrated amounts of cloud and water vapour [kg m-2])

Scattering index (SI) – e.g. Grody (1991, JGR)

- Simple SI used at ECMWF for SSMIS over land: 90 GHz – 150 GHz


v3703v22021 lnln TTcTTccLWP

cosTCWVLWPexp VapourCloud kk

Reasons to assimilate cloud and precipitation-related observations in global NWP

Extending satellite coverage: to gain more information on temperature and water vapour in cloudy regions

Improving cloud and precipitation analyses and short-range forecasts: assimilating cloud and precipitation directly

Inferring wind information through 4D-Var

Validating and constraining the model: confronting the model with observations

24ECMWF/EUMETSAT satellite course 2015: Microwave 2

Model Observations

Clear-sky assimilation


×

×

?

Model Observations

All-sky assimilation


All-sky assimilation components in 4D-Var

Observation minus first-guess* departures in clear, cloudy and precipitating conditions

Observation operator including cloud and precipitation (RTTOV) - TL/Adjoint

Moist physics - TL/Adjoint

Forecast model - TL/Adjoint

Control variables (winds and mass at start of assimilation window) optimised by 4D-Var


*FG, T+12, background…

Rest of the global observing system

Background constraint

28 ECMWF/EUMETSAT satellite

All-sky 4D-Var SSM/I - example

First guess departures (observation minus model)

All-sky observations (37GHz v-pol )

Is the zero-gradient issue a problem? No

Cloud

Total moisture

Microwave radiance

Total moisture

Cloud

Precipitation

Clear-sky

Model

Observation

Model

Observation


Mislocation between observations and model is a problem


Observed TB [K] First guess TB [K]

FG Departure [K](observation minus FG)

220km

Clear-clear

Cloud-cloud

Obs Cloud- FG clearObs Clear- FG cloud

Watch out for sampling error

Observations cloudy (47%):biased sampling

Observations or FGCloudy (59%):correct sampling

All-sky (100%)


Asymmetric and symmetric sampling

Cloud amountNormalised 37GHz polarisation difference

as a function of mean of observed and forecast cloud

as a function of forecast cloud

as a function of observed cloud

ECMWF/EUMETSAT satellite course 2015: Microwave 2

Slide 32

Mean channel 19v departures

[K]

Observation errors as a function of cloud amount


Mean of observed and FG cloud amountderived from 37GHz radiances

Standard deviation of

AMSR-E channel 24h departures

[K]

‘Symmetric’ observation error model

Gaussian

Departures4.3K

Non-Gaussianity


Departuressymmetric error


All-sky 4D-Var departures: Quality Control

SSM/I 37v departure Normalised by symmetric error

Assimilating observations in all-sky conditions

Essentials

- (4D-Var) Tangent linear and adjoint moist physics model

- Scattering radiative transfer code

Attention to “detail”: scattering parameters; cloud overlap

- Only assimilate in channels (and in areas) where the forecast model and the observation operator are accurate and are not affected by systematic errors

- Observation error model

smaller errors in clear skies and higher errors in cloudy and precipitating situations

- Symmetric treatment of biases, observation errors, quality control

Not essential, but still useful

- (4D-Var) Cloud and precipitation variables in the control vector


Applications of all-sky assimilation

Imager channels (e.g. 19, 24, 37, 89 GHz)

- TMI, SSMIS and (AMSRE): all-sky assimilation operational at ECMWF since 2009 over ocean surfaces

Water vapour sounding channels (e.g. 183 GHz)

- Over ocean, land and sea-ice

- SSMIS and MHS 183 GHz all-sky assimilation

- ATMS, MWHS-2 183 GHz all-sky in development

Temperature sounding channels (e.g. 50-60 GHz)

- Clear-sky approach remains the best for now

- AMSU-A channel 4 (52.8 GHz) is like an imager channel, with mainly a cloud sensitivity. Duplicates microwave imager information content.

- AMSU-A channel 5 (53.6 GHz) gained little benefit from all-sky assimilation in initial testing at ECMWF:

Not much additional coverage

Cross-talk between cloud and temperature signals

Scattering radiative transfer is relatively computationally expensive


Impact of all-sky SSMIS and TMI on wind 4 months of forecast verification against own analysis


Increased size of wind increments –short range “noise”

Normalised change in RMS forecast error in windCross-hatching indicates statistical significance

RMS error increased = bad (but not always!)

RMS error decreased = good

Up to 2-3% improvement in wind scores in the midatitudes


Slide 39

Clear-sky MHS

MHSbad

MHSgood


Slide 40

All-sky MHS

MHSbad

MHSgood

Cloud and precipitation in the microwave

Interaction of particles with microwave radiation

- Compute optical properties using DDA or Mie theory

Cloud-clearing and simple retrievals

- Window channel FG departures, polarisation difference, scattering index or LWP retrieval

Scattering radiative transfer simulations

- RTTOV-SCATT

All-sky assimilation

- Applicable to all imager and moisture channels: cloud, precipitation and water-vapour information

- Benefits to dynamical forecasts through 4D-Var tracing effect

- Temperature channels are best assimilated using clear-sky approach for the moment


microwave observations in the presence of cloud and ...cloud screening use clear-sky...

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