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Assessing observation impact using the adjoint of the GEOS-5 data assimilation system

This study uses the GEOS-5 data assimilation system to evaluate the impact of observations on analysis and forecast errors. The results show the value of different observation subsets and the limitations of linear approximations.

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Assessing observation impact using the adjoint of the GEOS-5 data assimilation system

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  1. Assessing observation impact using the adjoint of the GEOS-5 data assimilation system Yanqiu Zhu Ron Gelaro, Ron Errico, Ricardo Todling, Jing Guo, Rob Lucchesi

  2. OUTLINE • Introduction • Data assimilation adjoint theory • Adjoint-based observation impact on analysis • Adjoint-based observation impact on reducing forecast error • Comparison between Adjoint and OSE techniques • Conclusions

  3. Introduction • Quantify the “value” of observations • Extend adjoint sensitivity into observation space (Baker and Daley 2000, Langland and Baker 2004, Cardinali et al. 2004, etc) • A complementary tool of OSE (e.g., Lord et al. 2004; Kelly et al. 2004; English et al. 2004) 16-Jan-2003 00UTC All data: 1,178,200 observations

  4. Gain matrix • Linearized total analysis increment (neglecting impact of nonlinear operators in the inner loop) GSI analysis scheme Parrish and Derber 1992; Wu et al. 2002 Minimize: • Incremental approach where • Analytical forms of the analysis increments

  5. Data assimilation adjoint theory (gain matrix)  Sensitivity of the analysis with respect to observations: (Baker and Daley, 2000, …) adjoint of analysis scheme  Atmospheric forecast model:  Analysis solution:  Sensitivity of the response function with respect to observations: (observation space) (analysis space) (model space) is a forecast, is a forecast/analysis measure, is the adjoint forecast model

  6. inc. of Tv / u, all vertical levels, eastern North Pacific (NP) or United States (US) Observation impact on analysis increment Response function: Sensitivity of with respect to observations • Rawinsonde temperature observations at 500 hPa • Channel 5 brightness temperatures on NOAA-16 AMSU-A • GOES IR cloud drift zonal wind observations at 500 hPa Sensitivity on 5 August 00Z

  7. Analysis space Observation space Observation impact on analysis increment From we have

  8. satellite radiance conventional obs total obs Impacts of observing systems on JTNP during August 2004 Observation impact on analysis increment

  9. Observation Impact on Forecast Error Response function: where the forecast error measure (global dry energy, sfc-130hPa): 1st order approximation of in terms of vector d: 2nd order approximation of : 3rd order approximation of : …summed observation impact assimilation adjoint model adjoint …see Langland and Baker (2004), Errico (2007)

  10.  Accurate approximation of by adjoint observation impact is required in order to calculate meaningful observation impact of any arbitrary subset  The impacts of arbitrary subsets of observations (e.g., separate satellites, channels or locations) can be easily quantified by summing only the terms involving the desired elements of .  Independent subsets of observations contribute independently to the 1st order approximation …the observation improves the forecast …the observation degrades the forecast  The quadratic nature of the error measure leads to the necessity of considering nonlinear approximations of J  ambiguity in interpreting the impact of a particular subset … trade-off of obtaining better accuracy  The ADJ impact of any subset of observations is computed when the entire observation dataset is present in the assimilation system

  11. GEOS-5 Observation Impact Experiments Analysis System  3DVAR Gridpoint Statistical Interpolation (GSI)  0.5o resolution, 72 levels, 2 outer loops x 100 iterations  Adjoint:Exact line-by-line Forecast Model  GEOS-5: FV-core + full physics  0.5o resolution, 72 levels  Adjoint: FV-core1o resolution + simple dry physics Experimentation  6h data assimilation cycle, July 2005 and January 2006  30h forecasts from 18z and 24h forecasts from 00z to assess observation impact  Separate error response functions for the globe, NH, SH and tropics

  12. Accuracy of Observation Impact Estimate GEOS-5 July 2005 00z date (J/Kg)  …observations provide benefit (as a whole)  2nd and 3rd order estimates recover roughly 85% of actual impact  Possible sources of the difference - missing important physical parameterizations in the ADJ, dry energy form, and the restriction of validity period of the tangent linear approximation

  13. Observations that reduced the 24h forecast error: Observations that increased the 24h forecast error: Observations that had small impact on 24h forecast error Observation Impact on GEOS-5 24h Forecast Error 10 July 2005 00Z Impact of 500mb RAOB Temps Impact of AIRS Ch.221 Radiances Error Reduction Error Increase Error Reduction Error Increase

  14. Accumulated Raobs impact 00Z July 2005 Fraction of observations that improve forecast Observation impact (J/kg)

  15. AIRS Impact by channel (20-50N, 0-80E) Accumulated Observation Impact - AIRS AIRS January 2006 degrade Large positive impact over N.Pacific; region of large forecast error sensitivity improve AIRS July 2005  Positive impact in the southern oceans, but negative impact of AIRS observations over land…

  16. Total 24hr Forecast Error Reduction due to Observations July 2005 00UTC Global N. Hemisphere (20o-80o) (J/kg) S. Hemisphere (20o-80o) Tropics (20o-20o) (J/kg) GEOS-5 Adjoint Data Assimilation System

  17. Total 24hr Forecast Error Reduction due to Observations January 2006 00UTC Global N. Hemisphere (20o-80o) (J/kg) S. Hemisphere (20o-80o) Tropics (20o-20o) (J/kg) GEOS-5 Adjoint Data Assimilation System

  18. July 2005S. Hemisphere January 2006 N. Hemisphere Forecast Day Forecast Day Comparison between Adjoint and OSE techniques  The ADJ measures the impacts of observations in the context of all other observations present in the assimilation system, while the observing system is modified in the OSE (i.e., differs for each OSE member)  The ADJ measures the response of a single forecast metric to all perturbations of the observing system, while the OSE measures the effect of a single perturbation on all forecast metrics  errors in dry energy norm form are computed for OSE and compared with ADJ results • The ADJ is restricted by the tangent linear assumption (valid ~1-3 days), while the OSE is not  1-day OSE forecast results vs. ADJ observation impact results

  19. observations assimilated background forecast Error analysis forecast t 6h 00Z t +24h Comparison between Adjoint and OSE techniques (cont.)  The ADJ measures the impact of observations separately at every analysis cycle versus the background, while the OSE measures the total impact of removing data information accumulated in both the background and analysis

  20. (J/Kg) ? Comparison between Adjoint and OSE techniques (cont.) • The ADJ and OSE techniques produce a very similar qualitative pattern on the short-term forecast with some exceptions multiple OSEs 24h Forecast Error Energy -2 (J/Kg) July 2005 00z control observation impact Observation Count (millions)

  21. Comparison between Adjoint and OSE techniques (cont.) (J/Kg) 24h Forecast Error Energy control no satwnd (20N-20S) Exception 1: ADJ Satwnd impact is under-estimated July 2005 00z Global (J/Kg) no satwnd_tr Satwnd impact mainly due to data in tropics

  22. Define the fractional impact of observing system for each approach:  Measures the % decreasein error due to the presence of observing system with respect to the background forecast  Measures the % increase in error due to the removal of observing system with respect to the control forecast ‘Direct’ quantitative comparison of ADJ and OSEs  

  23. ADJ OSE Global N. Hemisphere (20o-80o) % S. Hemisphere (20o-80o) Tropics (20o-20o) % % Contributions to 24hr Forecast Error Reduction July 2005 Exception 2: Tropical impacts of all observing systems are under-estimated by ADJ technique

  24. Comparison between Adjoint and OSE techniques (cont.) ADJ OSE Exception 3: skill deteriorates rapidly in OSE when all the AMSUA are removed OSE July 2005 00z Global 24h Forecast Error Energy control no amsua1 (J/Kg) no amsua2 no amsua3 But with ADJ, the information in the background keeps the skill from dropping disproportionably % Contributions to 24hr Forecast Error Reduction

  25. Comparison between Adjoint and OSE techniques (cont.) Control No AMSUA No AIRS No Raob  The ADJ may help our understanding in the interactions and redundancies among various observing systems January 2006 Global Observations % Contribution to 24h forecast error reduction Removal of AMSUA results in large increase in AIRS (and other) impacts Removal of AIRS results in significant increase in AMSUA impact Removal of Raobs results in significant increase in impact of several obs types, with AIRS and Satwinds being a notable exceptions

  26. No Raob Comparison between Adjoint and OSE techniques (cont.) July 2005 Tropical Observations Control No AMSUA % Contribution to 24h forecast error reduction No Satwind Removal of AMSUA results in large increase in AIRS impact in tropics Removal of wind observations results in significant decrease in AIRS impact in tropics (in fact, AIRS degrades forecast without Satwinds!)

  27. Control Control No AMSUA No AIRS Comparison between Adjoint and OSE techniques (cont.) AIRS GEOS-5 July 2005 00z AMSU-A Only a small majority of the observations improve the forecast The fractions only change slightly in each pair

  28. Comparison between Adjoint and OSE techniques (cont.) Control AIRS channel impact (July 2005) No AMSUA2 Both magnitudes of beneficial/detrimental impacts from data are increased

  29. Comparison between Adjoint and OSE techniques (cont.) Control AMSUA3 channel impact (July 2005) No AIRS

  30. Conclusions  Data assimilation system adjoint provides an accurate and efficient tool for estimating observation impact on analyses and forecasts • computed with respect to all observations simultaneously • permits arbitrary aggregation of results by data type, channel, location, etc.  Applications to data quality assessment and selection, DAS behavior, understanding redundancies and gaps in the observing system  Complement and extend, but not replace, traditional OSEs as tools for assessing observation impact  Comparisons of impacts in different forecast systems should help clarify deficiencies in data quality vs. assimilation methodology, and hopefully provide useful feedback to data producers.

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