1. Considerations for the Physical Inversion of Cloudy Radiometric Satellite Observations

2. Outline 2 1 2 3 4 Microwave observation sensitivity to hydrometeors 1DVAR data assimilation preprocessing/considerations Accounting for cloud microphysical properties Future considerations and conclusions

3. Satellite Radiance Sensitivity 3 Upwelling Radiance Downwelling Radiance Surface-reflected Radiance Cloud-originating Radiance Surface-originating Radiance Scattering Effect Absorption Surface sensor Satellite data (depending on sensor characteristics) are sensitive to: - Atmosphere (temperature, water vapor) - Surface (ice, snow, land, ocean) - Hydrometeors (liquid, ice water) - Aerosol Aerosol Radiance

4. Considerations for Physical Inversion of Cloudy Observations 4 Handling of Cloudy Observations Macro-physical Properties: - Amount - Phase/Mixed phase - Profile vertical distribution - Type Micro-physical Properties: - Effective Radius - Density - Habit distribution - Particle size distribution Modulating Factors: - Emissivity - Beam Filling Factor (fraction) - Partial column Water Vapor - Layer Temperature Representation Considerations - Instrument Noise - Footprint size & shape - Biases - Calibration - Contamination (RFI, etc) - Geolocation uncertainties - Information content Observations Considerations - Optical properties - Surface characterization - Radiative Transfer (3D, scattering, etc) RT Modeling Considerations - Methodology (1D, 3D, 4D) - Stave vector composition - Covariance Matrix (Geophysical) - Covariance Matrix (Obs/RTM) - Jacobians - Resolution in time and space Consequences on Inversion

5. Microwave (MW) Sensitivity (1-330 GHz) 5 Frequency Correlation CLW/GWP/Rain H20H20TTH20H20H20H20

6. MW Channel Sensitivity -19GHz- (Case of Cold-Rain Profile) 6 Besides Rain & Ice Impact on Tb, Emissivity, Effective Radius (of Rain) & Cloud Fraction have an important impact on the simulation Delta TB is wrt Clear Sky

7. 7 At 37GHz, the Effective Radius of Ice starts playing a role at high amounts. Emiss. Effect is reduced Delta TB is wrt Clear Sky MW Channel Sensitivity -37GHz- (Case of Cold-Rain Profile)

8. MW Channel Sensitivity -50GHz- (Case of Cold-Rain Profile) 8 At 50GHz, the Effective Radius of Rain and Ice starts playing equal roles. Emissivity effect is further reduced. Ice Amount starts having an effect on Tb Delta TB is wrt Clear Sky

9. MW Channel Sensitivity -89GHz- (Case of Cold-Rain Profile) 9 At 89GHz, the emissivity has no impact at high rain/ice amounts, but still has a large impact in light precip. Ice amount has a significant impact Delta TB is wrt Clear Sky

10. 10 At 165GHz, the ice has a bigger role (amount and Reff). Emissivity effect is reduced to almost non-hydrometeor cases only. Fraction is also critical Delta TB is wrt Clear Sky MW Channel Sensitivity -165GHz- (Case of Cold-Rain Profile)

11. MW Channel Sensitivity -183GHz- (Case of Cold-Rain Profile) 11 At 183GHz, the Emissivity effect is un-noticeable. Fraction is important only for high amounts. Most important factor is Water Vapor Screening (TPW). Rain does not impact (amount or Reff). Ice amount is important. Delta TB is wrt Clear Sky

12. MW Channel Sensitivity 183+/- 10GHz- (Case of Cold-Rain Profile) 12 At 193GHz, the Emissivity effect is un-noticeable. Fraction is important only for high amounts. Water Vapor Screening (TPW) is no longer important. Ice amount& Reff important. Delta TB is wrt Clear Sky

13. Overall RTM Uncertainty 13 ECMWF 137 dataset (Eresmaa and McNally,2014) - Cloudy-sky (all hydrometeors present) minus clear-sky (no hydrometeors) - Simulations using ~15000 profiles from EC137 dataset over land and ocean. - Mean value, maxima/minima, 90 th and 10 th %-ile and quartiles are shown for the set of cases simulated. Large uncertainty across the MW spectrum due to assumptions/uncertainties of cloud microphysical properties

14. 14 1 2 3 4 Microwave observation sensitivity to hydrometeors 1DVAR data assimilation all-sky overview Assumptions and uncertainties for 1DVAR inversion Future considerations and conclusions

15. Challenges for 3DVAR DA 15 High Non-linearities, Discontinuities in space Challenging applicability of 3Dvar constraints when inverting/assimilating hydrometeor-impacted observations

16. Challenges for 4DVAR 16 High Non-linearities, Discontinuities in time Challenging applicability of 4Dvar constraints when inverting/assimilating hydrometeor- impacted observations

17. More Applicable for 1DVAR? 17 TB variation vs. hydrometeors is non-linear but is locally linear, therefore compatible with 1D variational inversion

18. MIIDAPS 1DVAR Preprocessor for Satellite DA 18

19. MIIDAPS Inversion Process 19 Cost Function Optimal Solution Locally Linear Cloudy Observation Considerations No bias correction Obs Errors inflated State vector initialized from regression or offline background Covariances computed from model or climatology 4 stream RT in scattering case

20. Use of All Channels 20 GWP TPWTSKIN RWP Retrieval of parameter as a function of 1DVAR iteration illustrating the convergence for Rain Water Path (RWP), Graupel Water Path (GWP), Total Precipitable Water (TPW), Skin Temperature (TSKIN) and 183 ±7 GHz Surface Emissivity. Legend displays which channels were used in the assimilation. GMI GWP with 165/183 GHz GMI GWP without 165/183 GHz

21. Simultaneous Inversion 21 Figures. Retrieval of parameter as a function of 1DVAR iteration illustrating the convergence for Rain Water Path (RWP), Graupel Water Path (GWP), Total Precipitable Water (TPW) and 183 ±7 GHz Surface Emissivity. ChiSq convergence metric printed in legend for each state vector configuration. RWPGWP TPW183 ±7GHz Em Setup: 1DVAR applied to simulated ATMS using all channels for assimilation Simulated TB has impacts from all parameters including rain/ice Retrieval is done using incremental state vector Result: Addition of T sounding helps the retrieval of ice, rain and TPW Rain/Graupel signal absorbed by emissivity when not in [X] Rain/ Ice retrieval is biased if other modulating factors not accounted for Assimilation in Cold Rain Case

22. 22 1 3 4 Microwave observation sensitivity to hydrometeors 1DVAR data assimilation all-sky overview Assumptions and uncertainties for 1DVAR inversion Future considerations and conclusions 2

23. State Vector Extension to R eff 23 Assume Rain/Ice 500 µm Assume Rain/Ice 1000 µm GFS T 400 mbMIIDAPS T 400 mbMIIDAPS-GFS CRTM allows for specification of layer hydrometeor effective radius. The MIIDAPS state vector was extended to account for effective radius to limit propagated errors from incorrect parameterization into other variables.

24. A note about background simulations 24 ECMWF LWPATMS OBS 31 GHzATMS OBS 165 GHz Prescribed Rain R eff ATMS FWD 31 GHzATMS FWD 165 GHz

25. Future Considerations The key, whether 1D, 3D, 4DVar DA/Inversion of radiances, is to reduce the uncertainty through constraining forward operator assumptions. Constrain through preprocessing/1DVAR, quasi-variational (information content/degrees of freedom) Through an a-priori (diagnosed variables from background, or ensemble DA) Even if we can perfectly model observations on a point by point basis, consistency needs to be maintained spatially in the analysis fields. 25 Reduce