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Rod Frehlich and Robert Sharman University of Colorado, Boulder RAP/NCAR Boulder

The Importance of Atmospheric Variability for Data Requirements, Data Assimilation, Forecast Errors, OSSEs and Verification. Rod Frehlich and Robert Sharman University of Colorado, Boulder RAP/NCAR Boulder Funded by NSF (Lydia Gates) and FAA/AWRP. In Situ Aircraft Data.

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Rod Frehlich and Robert Sharman University of Colorado, Boulder RAP/NCAR Boulder

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  1. The Importance of Atmospheric Variability for Data Requirements, Data Assimilation, Forecast Errors, OSSEs and Verification Rod Frehlich and Robert Sharman University of Colorado, Boulder RAP/NCAR Boulder Funded by NSF (Lydia Gates) and FAA/AWRP

  2. In Situ Aircraft Data • Highest resolution data • Many flights provide robust statistical description (GASP, MOZAIC) • Reference for “truth”

  3. Spatial Spectra • Robust description in troposphere • Power law scaling • Valid almost everywhere

  4. Structure Functions • Alternate spatial statistic • Interpretation is simple (no aliasing) • Also has power law scaling • Structure functions (and spectra) from model output are filtered • Corrections possible by comparisons with in situ data • Produce local estimates of turbulence defined by εor CT2 over LxL domain

  5. RUC20 Analysis • RUC20 model structure function • In situ “truth” from GASP data • Effective spatial filter (3Δ) determined by agreement with theory

  6. UKMO 0.5o Global Model • Effective spatial filter (5Δ) larger than RUC • The s2 scaling implies only linear spatial variations of the field

  7. DEFINITION OF TRUTH • For forecast error, truth is defined by the spatial filter of the model numerics • For the initial field (analysis) truth should have the same definition for consistency • Measurement error • What are optimal numerics?

  8. Observation Sampling Error • Truth is the average of the variable x over the LxL effective grid cell • Total observation error • Instrument error = x • Sampling error = x • The instrument sampling pattern and turbulence determines the sampling error

  9. Sampling Error for Velocity and Temperature • Rawinsonde in center of square effective grid cell of length L

  10. UKMO Global Model • Rawinsonde in center of grid cell • Large variations in sampling error • Dominant component of total observation error in high turbulence regions • Very accurate observations in low turbulence regions

  11. Optimal Data Assimilation • Optimal assimilation requires estimation of total observation error covariance • Requires calculation of instrument error which may depend on local turbulence (profiler, coherent Doppler lidar) • Requires climatology of turbulence • Correct calculation of analysis error

  12. Adaptive Data Assimilation • Assume locally homogeneous turbulence around analysis point r • forecast • observations

  13. Optimal Analysis Error • Analysis error depends on forecast error and effective observation error • forecast error • effective observation error (local turbulence)

  14. Analysis Error for 0.5o Global Model • Instrument error is 0.5 m/s • Large reduction in analysis error for b=3 m/s

  15. Implications for OSSE’s • Synthetic data requires local estimates of turbulence and climatology • Optimal data assimilation using local estimates of turbulence • Improved background error covariance based on improved analysis • Resolve fundamental issues of observation error statistics (coverage vs accuracy) • Determine effects of sampling error (rawinsonde vs lidar)

  16. Implications for NWP Models • Include realistic variations in observation error in initial conditions of ensemble forecasts • Determine contribution of forecast error from sampling error • Include climatology of sampling error in performance metrics

  17. Future Work • Determine global climatology and universal scaling of small scale turbulence • Calculate total observation error for critical data (rawinsonde, ACARS, profiler, lidar) • Determine optimal model numerics • Determine optimal data assimilation, OSSE’s, model parameterization, and ensemble forecasts • Coordinate all the tasks since they are iterative

  18. Estimates of Small Scale Turbulence • Calculate structure functions locally over LxL square • Determine best-fit to empirical model • Estimate in situ turbulence level and ε ε1/3

  19. Climatology of Small Scale Turbulence • Probability Density Function (PDF) of ε • Good fit to the Log Normal model • Parameters of Log Normal model depends on domain size L • Consistent with large Reynolds number turbulence

  20. Scaling Laws for Log Normal Parameters • Power law scaling for the mean and standard deviation of log ε • Consistent with high Reynolds number turbulence

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