Physically-based satellite data assimilation and fuzzy verification in numerical simulations

1. Physically-based satellite data assimilation and fuzzy verification in numerical simulations Gad Levy1and Deborah Sulsky2 1 NorthWest Research Associates, Seattle, WA, USA 2 Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico, USA http://www.nwra.com/people.php#gadlevy March, 17 2015: NCEP

2. Acknowledgements. Eary part of this work was supported by the National Science Foundation (under grants ARC-0621173 and ATM- 0741832). Max Coon, who passed away on Feb. 9, 2010, initiated, inspired and guided our work on sea ice. We miss him. Barnabas Bede, Luciana Taka Gomez, Andrew Geiss

3. Outline • Problems/challenges in assimilation/validation addressed • Evaluation of lower dimensional features (fuzzy verification) • Proposed assimilation and validation algorithm • Model testing • Assimilation/initialization experiment • Results • Conclusions

4. Challenges in Assimilation & Validation addressed • The analyzed field, based on the data is not a model realizable state • Will produce noise if used to initialize • Assimilation systems do not have a simple, quantitative measure of representing features contained in bulk simulation (lower dimensional features). • The observed (remote-sensing) variables do not match the model variables, requiring parameterizations are not consistent with the data or the physics

5. Deficiencies of RMS metrics RMSE penalizes models that are not accurate in the location twice.

6. Lower-dimensional features (LF) • Features not directly measured/ resolved by observing systems or most models • can be related to model resolvable physical or material properties. • Challenge to assimilate using standard practice of “innovations” (observation increments). • Challenge to validate (calls for fuzzy verification).

7. Lower-dimensional features Examples ERS-1 SAR image acquired on 20 May 1994 at 14:20 UTC over the Pacific Ocean east of Taiwan; orbit: 14874, frame: 2364, frame center: 23° 01'N, 121° 41'E, imaged area: 100 km x 100 km. A ship travelling northward (bright spot at the front of the black line) discharging oil. The oil disperses with time causing the oil trail to widen

8. LdF Examples Cyanobacterial bloom in the Baltic Sea, MODIS image

9. LdF ExamplesNear-Equatorial Convective Regimes

10. Linear Kinematic Features • Represent discontinuities in the sea-ice (e.g., leads or ridges) • In data come from the RADARSAT Geophysical Processor System (RGPS) developed by Polar Remote Sensing Group at JPL • In model, predicted through initiation and opening of leads based on the kinematics associated with strong discontinuities

11. Feature extraction in SAR • At an initial time, a set of points forming a regular grid is located in the SAR data sets • In subsequent images (approx. every 3-days), original points are found again using area-based and feature-based tracking • Procedure provides displacements for each point, motion of the points, deformation, • Determine a jump in displacement and its orientation that account best for the observed deformation of an RGPS cell based on kinematics associated with strong discontinuities

12. Input: Wind Thermodynamics Model Equations: Momentum Stress-strain Failure surface Thickness dist., G Strength from G Air stress (from wind) Sea-Ice (Fram) Model Used Output: Velocity (Disp.) E & D cells* E cell: strain D cell: Lead , U Strength Failure surface Stress state *Each cell is elastic (E) with associated strain, or failed decohesion (D) with a lead direction and displacement 

13. Model outputs • Motion • Lead: • o Time of initiation and age • o orientation • o mode (opening and shear) • Stress resultants: • o normal • o shear • Ridge formation • o ice thickness distribution Schreyer, H. L., L. B. Munday, D. L. Sulsky, M. D. Coon and R. Kwok, 2006. J. Geophys. Res., 111, C11S26, doi:10.1029/2005JC003334. Coon, M., R. Kwok, G. Levy, M. Pruis, H. Schreyer, and D. Sulsky, 2007. J. Geophys. Res., 112, C11S90, doi:10.1029/2005JC003393

14. Features of MPM (Material Point Method) • Dual description of the continuum: Lagrangian (material points) and computational mesh. The unconnected material points represent the geometry rather than the mesh. Allows large deformations, including fracture. • The convective phase of the algorithm is performed by Lagrangian material points which carry position, mass, velocity… Properties transported without error. Multiple materials easily represented. • The interaction between material points is solved using a finite element discretization on a mesh (cost is linear in the number of material points) • Information is transferred between the material points and the mesh by interpolation (only changes are interpolated, keeping numerical dissipation relatively small) D. Sulsky, H. Schreyer, K. Peterson, M. Coon and R. Kwok, 2007. JGR, 112, C02S90, doi:10.1029/2005JC003329

16. Fuzzy Verification • metrics to measure model accuracy in representing linear features are tested. • Metrics circumvent requirement that both observations and model variables be commensurate (measured with the same units) by considering features of interest frequencies. • Substituted in a common skill score Levy, G., M. Coon, G. Nguyen, and D. Sulsky (2008), Geophys. Res. Lett., doi:10.1029/2008GL035086

17. Metric used in assimilation experimentFor L features of interest and N spatial segments of the domain frequency distance function RMS Index of Agreement P i,j and o i,j are predicted & observed feature frequencies, D i,j is a normalized frequency function, w are weights Define a general skill score

18. Other metrics/procedures testedFuzzification avoids drawbacks

19. Definition of a fuzzy set

20. A fuzzy set can model linguistic concepts

21. Fuzzy Operations

22. Properties of Fuzzy similarities

23. Examples of Fuzzy similarities

29. Assimilation experimental design • A control run, and an experimental run of sea-ice in Beaufort Sea over 16 days at 10 km resolution • Initial and boundary values of all model variables and parameters are the same • Experimental simulation goes through a one-step assimilation during day 54, where information on the pattern of leads from RGPS at 10-km resolution is used to predispose the model

30. Sixteen day run - B. Sea (Feb.-March, 2004) • Observations from SAR (RADARSAT 1) • Model run w/o assimilation • Model run with assimilation • Observations from SAR Levy, G., M. Coon, G. Nguyen, and D. Sulsky (2010), Geosci. Model Dev., doi:10.5194/gmdd-3-1-2010 http://www.geosci-model-dev-discuss.net/3/517/2010/gmdd-3-517-2010.html

37. Skill Score

38. Conclusions • Much better skill metrics • New assimilation/initialization results in positive prediction skill within one day as opposed to 5 days w/o assimilation • Skill score significantly improves • Can be regarded as a poor-man’s 4D assimilation, or a physically based ‘nudging’ • Potential application for ‘bogusing’, tested for climate classification of monsoon/ITCZ Thank You!

39. Fuzzy OR Double ITCZs and the Indian Summer Monsoon Geiss, Levy

40. Fuzzy Filters Σmin(OLR,Filter) / Σmax(OLR,Filter) Double ITCZs and the Indian Summer Monsoon Geiss, Levy

41. Results of Climate Fuzzy Classification (IO convective regimes)