1. Cloud and precipitation best estimate… …and things I don’t know that I want to know Robin Hogan University of Reading

2. 3. Compare to observations Check for convergence Unified retrieval Ingredients developed Done since December Not yet developed 1. Define state variables to be retrieved Use classification to specify variables describing each species at each gate Ice and snow: extinction coefficient, N 0 ’, lidar ratio, riming factor Liquid: extinction coefficient and number concentration Rain: rain rate, drop diameter and melting ice Aerosol: extinction coefficient, particle size and lidar ratio 2a. Radar model With surface return and multiple scattering 2b. Lidar model Including HSRL channels and multiple scattering 2c. Radiance model Solar & IR channels 4. Iteration method Derive a new state vector: Gauss-Newton or quasi- Newton scheme 2. Forward model Not converged Converged Proceed to next ray of data 5. Calculate retrieval error Error covariances & averaging kernel

3. CloudSat Calipso Unified retrieval Ice extinction coefficient Rain rate Aerosol extinction coefficient

4. Simulated EarthCARE Higher sensitivity than CloudSat gives strikingly better sensitivity to tropical cirrus This case perhaps can form the basis for some ECSIM and Doppler simulations for an EarthCARE Bull Am Met Soc paper CloudSat EarthCARE CPR

5. Extending ice retrievals to riming snow Heymsfield & Westbrook (2010) fall speed vs. mass, size & area Brown & Francis (1995) ice never falls faster than 1 m/s Brown & Francis (1995) 0.9 0.8 0.7 0.6 Retrieve a riming factor (0-1) which scales b in mass=aD b between 1.9 (Brown & Francis) and 3 (solid ice)

6. Simulated observations – no riming

7. Simulated retrievals – no riming

8. Simulated retrievals – riming But retrieval is completely dependent on how well we can model scattering by rimed snowflakes!

9. There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know. Donald Rumsfeld

10. A Rumsfeldian taxonomy The known knowns, things we know so well no error bar is needed –Drops are spheres, density of water is 1000 kg m -3 The known unknowns, things we can explicitly assign an well- founded error bar to in a variational retrieval –Random errors in measured quantities (e.g. photon counting errors) –Errors and error covariances in a-priori assumptions (e.g. rain number conc. parameter N w varies climatologically with a factor of 3 spread) The unknown unknowns where we don’t know what the error is in an assumption or model –Errors in radiative forward model, e.g. radar/lidar multiple scattering –Errors in microphysical assumptions, e.g. mass-size relationship –How do errors in classification feed through to errors in radiation? –How do we treat systematic biases in measurements or assumptions? (also the ignored unknowns that we are too lazy to account for!) How can we move more things into the “known unknowns” category?

11. Number concentration Size distribution width/shape Particle shapeRadar scattering & absorption Lidar scattering & absorption Warm liquid droplets Miles et al. (2000) Many aircraft campaigns SphereMie Supercooled droplets A few aircraft studies? Same as for warm droplets? SphereAttenuation unknown! Mie DrizzleAbel and Boutle (2012) Aircraft studies? SphereMie RainMany distrometer studies Illingworth & Blackman (2002) Spheroid, known aspect ratio T-matrix (Mie OK too) Mie is OK IceDelanoe and Hogan (2008) Delanoe et al. (2005), Field et al. (2005) Aggregate aspect ratio 0.6 Spheroid agrees with obs (Hogan et al. 2012) Retrieved lidar ratio encapsulates variations Snow (possibly rimed) Same as ice? How do we represent riming? Scattering uncertain! Lidar ratio encapsulates variations Melting iceLies between snow & rain? Very uncertain Attenuation uncertain! Ignore AerosolMany aircraft campaigns Dry aerosol shape uncertain IgnoreLidar ratio encapsulates variations

12. Melting layer: modelling Fabry and Szyrmer (1999) found 10 dB spread in melting-layer reflectivity at 10 GHz although their “Model 5” agreed best with obs But what about 94-GHz attenuation? What we really need is PIA through the melting layer versus rain rate, with an error

13. Haynes et al. (2009) The same Szymer and Zawadzki (1999) model Rain rate 2 mm h -1 6-7 dB 2-way attenuation Top of melting layer Base of melting layer

14. Matrosov (2008) 2-way radar attenuation in dB is 2.2 times rain rate in mm h -1 Attenuation at 2 mm h -1 is 5-5.5 dB We need observational constraints! E.g. aircraft flying above and below melting layer, each with 94-GHz radar and the one below with airborne distrometer Or multi-wavelength ground-based technique? Matrosov (IEEE Trans. Geosci. Rem. Sens. 2008)

15. Snow What’s the 94 GHz backscatter cross-section of this? Spheroid model works up to D ~, but not for larger particles Rayleigh-Gans approximation works well: describe structure simply by area of particle A(z) as function of distance in direction of propagation of radiation Area of slice through particle A(z) Simulated aggregate (Westbrook et al.)

16. Self-similar Rayleigh Gans approx. A spheroid has a very similar A(z) to the mean A(z) over many snow aggregates: but for 1 cm snow at 94 GHz, the spheroid model underestimates backscatter by 2-3 orders of magnitude! Radiation “resonates” with structure in the particle on the scale of the wavelength, leading to a much higher backscatter, on average Power spectrum of this structure shows that these aggregates are “self similar” An equation has been derived for the mean backscatter cross-section of an ensemble of particles But all this depends on the realism of the simulated aggregates! Can we test observationally? Hogan and Westbrook (in preparation)

17. Supercooled water absorption No laboratory observations of 10-1000-GHz absorption of water colder than –6°C! All models in the literature are therefore an extrapolation, and unsurprisingly they differ significantly This is of most concern for microwave radiometry For EarthCARE, it is of concern in convective clouds, but very unclear whether the observations can usefully tell us about supercooled water in these clouds anyway; perhaps as a contribution to PIA in addition to rain? Stefan Kneifel et al (submitted)

18. Summary: the unknown unknowns We need a best estimate and error for the following: Snow backscatter cross-section at 94 GHz –“Self-Similar Rayleigh Gans” equation: test with multi-wavelength radar? Structure and radar scattering of riming particles –How do we represent the continuous transition between low-density aggregates and high density graupel, and validate observationally? Melting-layer radar attenuation versus rain rate –Key issue for interpreting PIA in rain: need observational constraints Super-cooled water in convective clouds –Radar absorption unknown, as well as vertical distribution Lidar backscatter of complex ice and aerosol shapes –Is it sufficient to simply retrieve lidar ratio from the HSRL and so bypass the difficulty in modelling the scattering of such particles? A comprehensive algorithm inter-comparison project would also help to identify unknown unknowns!

20. Examples of snow Examples of snow 35 GHz radar at Chilbolton 1 m/s: no riming or very weak 2-3 m/s: riming? PDF of 15-min-averaged Doppler in snow and ice (usually above a melting layer)

21. Simulated observations – riming

22. Power spectrum of snow structure

23. New formula for backscatter Rayleigh-Gans formula: Fourier-like decomposition of A(z): Assume amplitudes decrease at smaller scales as a power-law Formula for backscatter: –Wavenumber k –Volume V –Radius z max –Power-law parameters  & 

24. Prior information about size distribution Radar+lidar enables us to retrieve two variables: extinction  and N 0 * (a generalized intercept parameter of the size distribution) When lidar completely attenuated, N 0 * blends back to temperature- dependent a-priori and behaviour then similar to radar-only retrieval –Aircraft obs show decrease of N 0 * towards warmer temperatures T –(Acually retrieve N 0 */  0.6 because varies with T independent of IWC) –Trend could be because of aggregation, or reduced ice nuclei at warmer temperatures –But what happens in snow where aggregation could be much more rapid? Delanoe and Hogan (2008)