Uncertainty Quantification for GPM-era Precipitation Measurements Yudong Tian

1. Uncertainty Quantification for GPM-era Precipitation Measurements Yudong Tian University of Maryland & NASA Goddard Space Flight Center Collaborators: Ling Tang, Rebekah Esmaili Christa Peters-Lidard, Bob Adler, George Huffman, Joe Turk, Bob Joyce, Xin Lin, Ali Behrangi, Kuo-lin Hsu, Takuji Kubota, John Eylander, Matt Sapiano, Viviana Maggioni, Emad Habib, Huan Wu EGU, 30 April, 2014

2. Outline What we learned from TRMM-era measurements -- “The Error Structure” 1. concepts and procedures 2. error composition 3. systematic & random errors Applications of the Error Structure 4. scaling of errors 5. sources of errors What error structure to expect with GPM-era measurements

3. Procedure to quantify uncertainty Step 1: Get a reference dataset 3B42 (mm/day) It is all uncertain if we know no truth Truth (mm/day) Measurements can be validated Truth If truth is available …

4. Procedure to quantify uncertainty Step 2: Error decomposition (Tian et al., 2009) hits (H) false precip (F) 3B42 (mm/day) Truth (mm/day) missed precip (-D) (total error) (hit error) (missed) (false) E = H – D + F

5. Procedure to quantify uncertainty Step 3: Separate systematic and random error E= H – D + F systematic error (θ) 3B42 (mm/day) random error (σ) Truth (mm/day)

6. The Error Structure unifies uncertainty definition and quantification Total Error Hits (H) Systematic error (θ) False (F) Random error (σ) Missed (-D) Uncertainty quantification = ( -D, F, θ,σ )

7. Total Error E E = R – Rref

8. Error Decomposition Scheme (total error) (hit error) (missed) (false) E = H – D + F (Tian et al., 2009)

9. Error Decomposition, Winter (DJF) (total error) (hit error) (missed) (false) E = H –D + F 3B42 3B42RT CMORH PERS’N NRL

10. Determining the Error Structure – next step, hits error Total Error systematic error (θ) Hits (H) 3B42 (mm/day) False (F) random error (σ) Truth (mm/day) Missed (-D)

11. Xi Xi Ti Ti Hit error (H) is multiplicative (Tian et al., 2013) Additive error model Multiplicative error model  11

12. Two parameters quantify systematic error β systematic error α: scale error (ideal: 1) β: shape error (ideal: 1) TMPA 3B42 TMPA 3B42RT NOAA Radar What do α, β, and σ mean? ln(α) 12

13. One parameter quantifies random error Random error σ: (ideal: 0) TMPA 3B42 TMPA 3B42RT NOAA Radar 13

14. Procedure of uncertainty quantification – 3 steps to the Error Structure Total Error Hits (H) Systematic error (α, β) False (F) Random error (σ) Missed (-D) Uncertainty quantification = ( -D, F, α, β,σ )

15. Scaling of errors: how Error Structure changes with space/time scales Total Error Hits (H) Systematic error (α, β) False (F) Systematic error (α,β) False (F) Random error (σ) Random error (σ) Missed (-D) Missed (-D)

16. How systematic and random errors vary with space/time scales scale error ln(α) scale error ln(α) spatial scale  time scale  Systematic errors (α, β) shape error (β) shape error (β) random error (σ) random error (σ) Random errors σ

18. Errors can be traced back to Level-2 retrievals (Tang, Tian & Lin, 2013; Poster #Z42 today) AMSR-E/TMI/SSMI SSMIS AMSU-B MHS

19. Summary What we learned from TRMM-era measurements: The Error Structure and procedures to determine it 1. concepts and procedures 2. error composition 3. separation of systematic & random errors 4. scaling of errors 5. sources of errors Total Error Hits (H) Systematic error (α, β) False (F) Random error (σ) Missed (-D)

20. Total Error Hits (H) Systematic error (α, β) False (F) Random error (σ) Missed (-D)

21. Extra slides

22. Error can be further decomposed: • Decomposition of errors: • The 3 components can be proved to be independent to one another.

23. Over US, reliable reference data are available 4 ground-based datasets 6 satellite-based datasets

24. Errors are season/region-dependent over United States US West US East Winter Summer

25. Ground-based observations are patchy and sparse

26. Methodology 1: Using measurement spread Uncertainty: range of disagreement among independent measurements of the same physical quantity Suitable when “ground truth” is not available 26

27. Uncertainties are season/region-dependent Uncertainties over the globe: Winter and Spring Winter Summer

28. Ensemble mean of global precipitation Satellite-based observations enable global study of precipitation Winter Summer

29. Outline 1. Overview of global precipitation measurements 2. Uncertainty in precipitation – the story of an evolving paradigm 3. Efforts to improve global precipitation observations

30. Semi-independent satellite-based datasets

31. Several satellite-based, global, high-resolution datasets are available

32. Uncertainties also depend on rain rate – light rain, high uncertainty

33. Basic characteristics of satellite-based precipitation uncertainty • Depend on rain rate: ~25% heavy rain, ~100% light rain • Depend on region: high latitude, snow-cover, > 100% • Depend on season: winter > summer

34. Methodology 2: when ground truth is available (e.g., over U.S.) E = R - R0 Error = Measurement - Truth

35. Methodology 1: Using measurement spread when no ground truth Methodology 2: when ground truth is available (e.g., over U.S.) E = R - R0 Error = Measurement - Truth Methodology 3: Error decomposition (total error) (hit bias) (missed) (false) E = H – D + F

36. Outline 1. Overview of global precipitation measurements 2. Uncertainty in precipitation – the story of an evolving paradigm 3. Efforts to improve global precipitation observations

37. Precipitation over snow-covered surfaces is highly uncertain

38. West East Time series of error components. They sometimes enhance, sometimes cancel each other

39. What we do not know affects what we know Information Knowns Knowledge Signal Deterministic Systematic errors Uncertainty Unknowns Ignorance Noise Stochastic Random errors Uncertainty determines reliability of information

40. What about NWP forecasts?

41. Model-predicted measurements Comparison of data distributions Actual measurements The multiplicative error model predicts better Additive Model Multiplicative Model