Microwave observations in the presence of cloud and precipitation

Slide 1

Microwave observations in the presence of

cloud and precipitation

Alan Geer

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

Niels Bormann

Slide 2

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

Slide 3

Size parameter

Atmospheric particles and microwave radiation

30 GHz frequency ↔ 10mm wavelength (λ)

Particle type Size range, r Size parameter, x Scattering solution

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



r

Slide 4

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):

Slide 5



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

Slide 6

Scattering properties – single particles



Scattering cross-section: [m

2

_]

- the amount of scattering as an equivalent “area”



Absorption cross-section: [m

2

_]

- particles can absorb as well as scatter radiation



Scattering phase function:

- the amount of scattering in a particular direction (expressed in

s



a



)

,

(





P

Slide 7



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

s a e











s a s s

_

_









Slide 8

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)

• ω

_s

- 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 radiative

transfer (discretized on the vertical grid):

   

   









_

 

 

      ˆ 1 4 ( ˆ , ˆ ') ˆ ' ' ˆ d I P B I d dI _s s ) ' ˆ , ˆ (  P

ˆ

Slide 9



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:

- ω

_s

= 0 , so

- we can do each layer sequentially

Radiative transfer solvers

Scattering phase

function

   

















_





 















ˆ

1

4

₄

(

ˆ

,

ˆ

'

)

ˆ

'

'

ˆ

d

I

P

B

I

d

dI

_s s

   

I

B

d

dI









ˆ

_ˆ



 

ˆ I

 

ˆ ' I

Slide 10

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

Slide 11 Single

scatter albedo

Rain and snow flux [g m2 _s-1_]

Cloud mixing ratio [0.1 g kg-1_] Extinction coefficient β_[km-1] e Asymmetry

Snow

Rain Water cloud

Altitude [km]

Cloud and precipitation at 91 GHz

Slide 12

Cloud and precipitation at 91 GHz

Strong scattering in deep convection

R ai n S n o w C lo u d SSA [0-1] No. of emissions To sensor [km] [k m ]

Slide 13

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

Slide 14

AMSU-A channel 3 departures for cloud screening

50.3 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

Slide 15

AMSU-A channel 3 departures for cloud screening

50.3 GHz observation minus clear-sky first guess, ocean surfaces

FG departure [K]

3K limit

Warm tail = cloud

20% of observations

removed

Slide 16

AMSU-A channel 3 departures for cloud screening

50.3 GHz observation minus clear-sky first guess (bias corrected), ocean surfaces

Slide 17

AMSU-A channel 4 departures for cloud screening

52.8 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

Slide 18

AMSU-A channel 4 departures for cloud screening

52.8 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

Slide 19

An approximate radiative transfer equation for

window channels (no scattering)







T

_A

T

_S



T

_A

T





1





(

1





)







(

1





)



,

S

T

A

T

)

1

(





Surface temperature, emissivity A

T

)

1

(





Upwelling atmospheric contribution Downwelling atmospheric contribution S

T



Observed brightness temperature



1





(

1



)

T

_A







Reflected downwelling radiation Surface emission



Atmospheric transmittance

Slide 20

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

2

(

1

)



0









 T

T

Observed TB at frequency ν Surface emissivity Atmospheric transmittance

Slide 21

Polarisation difference



Observe v and h polarisations separately:



Compute the difference in brightness temperature



1

2

(

1

)



0 V V

T

T













1

2

(

1

)



0 H H

T

T













_{V H}



H V

T

T

T





₀



2







Slide 22

Polarisation difference at 37 GHz (SSMIS)

37v

[K]

37h

[K]

37v -37h

[K]

Slide 23

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



_{0 22v}



₃



_{0 37v}



2 1

c

ln

T

T

c

ln

T

T

c

LWP





















Slide 24

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

Slide 25 Model Observations

Clear-sky assimilation



×

×

?

Slide 26 Model Observations

All-sky assimilation









Slide 27

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

Slide 28

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

First guess departures (observation minus model)

All-sky observations (37GHz v-pol )

Slide 29

Is the zero-gradient issue a problem? No

Cloud

Total moisture

Microwave

radiance

Total moisture

Cloud

Precipitation

Clear-sky

Model

Observation

Model

Observation

Slide 30

Mislocation between observations and model

is a problem

Observed TB [K]

First guess TB [K]

FG Departure [K]

(observation minus FG)

Slide 31

Clear-clear

Cloud-cloud

Obs Cloud- FG clear

Obs Clear- FG cloud

Watch out for sampling error

Observations

cloudy (47%):

biased sampling

Observations or FG

Cloudy (59%):

correct sampling

All-sky (100%)

Slide 32

Asymmetric and symmetric sampling

Cloud amount

Normalised 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

Mean

channel 19v

departures

[K]

Slide 33

Observation errors as a function of

cloud amount

Mean of observed and FG cloud amount

derived from 37GHz radiances

Standard

deviation of

AMSR-E

channel 24h

departures

[K]

‘Symmetric’

observation

error model

Slide 34

Gaussian

Departures

4.3K

Non-Gaussianity

Departures

symmetric error

Slide 35

All-sky 4D-Var departures: Quality

Control

Slide 36

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

Slide 37

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

Slide 38

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

wind

Cross-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

MHS good

Slide 40

All-sky

MHS

MHSbad

MHS good

Slide 41

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