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Issues Regarding the Assimilation of Precipitation Observations

Issues Regarding the Assimilation of Precipitation Observations Dr. Ronald M. Errico Goddard Earth Sciences Technology and Research Center (Morgan State University, Maryland) Global Modeling and Assimilation Office (NASA). Outline

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Issues Regarding the Assimilation of Precipitation Observations

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  1. Issues Regarding the Assimilation of Precipitation Observations Dr. Ronald M. Errico Goddard Earth Sciences Technology and Research Center (Morgan State University, Maryland) Global Modeling and Assimilation Office (NASA)

  2. Outline • 1. Bayesian considerations • 2. Issues peculiar to precipitation assimilation • Examples of several issues • 4. Summary and recommendations

  3. Bayesian Considerations

  4. Implications of the Bayesian Approach • We see that both instrument and observation operator errors should be considered. • Results may depend on shapes of distributions, not only their means and variances. • 3. Multi-modality of the PDF can occur, particularly due to • non-linearity of the forward observation operator • We see that selection of a “best” analysis can be somewhat ambiguous.

  5. Some issues peculiar to precipitation assimilation (Examples to follow) 1. Distribution of precipitation errors is likely non-Gaussian. 2. Precipitation forward model error is likely large! 3. Multi-modal cost functions are likely. 4. Minimization of cost function may be poor objective. 5. Results may be very sensitive to prior statistics. 6. Straight-forward adjoint models of convection may be useless. 7. Common descent algorithms may be useless. 8. Results may be sensitive to precipitation type. 9. Possible incompatibility with gravity wave constraints.

  6. The distribution of precipitation Kedem and Chiu 1986

  7. From George Huffman

  8. Special treatment of 0 From Errico et al. 2000 QJRMS

  9. A possible problem with use of logs in the cost function Note that special treatment of 0 values are required.

  10. Example of Model Error: Errico et al. QJRMS 2001 6-hour accumulated precip. With 3 versions of MM5 Contour interval 1/3 cm (0 contour omitted) Kain - Fritsch Betts - Miller Grell

  11. PDF of differences Grell vs. Kain-Fritsch schemes Normalized PDFs of Model “errors” PDF of log of ratios Gaussian reference Errico et al. 2001 QJRMS

  12. Jacobians of Precipitation RAS scheme ECMWF scheme BM scheme Fillion and Mahfouf 1999 MWR

  13. Validation of a Tangent Linear Model

  14. Tangent linear vs. nonlinear model solutions TLM NLM Errico and Raeder 1999 QJRMS 60x small pert NLM

  15. Statistically-Based Sub-Grid Parameterization r q=qs | - r=0 q

  16. Dependence on precipitation type Fillion and Mahfouf 1999 MWR

  17. Adjoint-derived, optimal perturbations Errico, Raeder and Fillion, 2003 Tellus

  18. Vort optimized Impacts for adjoint- derived optimal perturbations for forecasts starting indicated hours in the past. Errico et al. 2003 Tellus Rn Optimzed Rc optimzed

  19. Posterior (analysis) PDF of 1DVAR of Convection 4 Conditional PDF 0 T-2 -4 -4 0 4 T-1 (standard deviations)

  20. 6-hour forecast Full Field Gravitational-mode field Contour interval 0.0025 mm/K

  21. Review of state-of-the-art at ECMWF

  22. The apparent neglect of many fundamentals Few statistical considerations background estimates ignored background error correlations ignored observations considered too accurate (and Gaussian) representativeness (forward model) error ignored Few balance considerations univariate error statistics unbalanced reference states Limited evaluation limited cases limited measures Some strange results ultra rapid convergence rates little decrease of norm of J-gradient

  23. Convergence of 4DVAR ECMWF 2002 Tsuyuki 1996 Navon 1999 ECMWF 2002

  24. Summary • I am confused! • How can so many apparently fundamental aspects of the • problem be neglected, yet such good results be reported? • Only in rare cases is enough information provided to help • explain question 2. • Since only an improvement over some baseline is required, • it is not necessary that “correct” procedures are used, just • “useful” ones. • Successes may reveal more about the baseline results than • about the correctness of a new assimilation procedure. • With both observation and forward model errors likely • very large, what should be a realistic expectation of the • usefulness of precipitation information and how can this • be realized?

  25. Recommendations 1. Be skeptical. 2. Ask lots of questions. 3. Consider Bayesian implications. 4. Determine reasonable error estimates. 5. Estimate what issues are generally important. 6. Explain results. 7. Encourage research at research institutions. 8. Entrain some interested experts.

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