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New Reference Atmosphere for COSMO Model

This paper presents a new reference atmosphere for the COSMO model, addressing limitations of the existing atmosphere. Tests comparing different cores and approximation methods are performed. Results show improved accuracy and increased vertical extent of the model domain.

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New Reference Atmosphere for COSMO Model

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  1. Günther Zängl, DWD A new reference atmosphere for the COSMO modelGünther ZänglDeutscher Wetterdienst, Offenbach, Germany

  2. Günther Zängl, DWD • Overview • Motivation of the new reference atmosphere and description • Tests considering its impact, including a comparison between Leapfrog and Runge-Kutta cores • Comparison with impact of unapproximated pressure tendency equation (Lucio Torrisi; see subsequent talk)

  3. Günther Zängl, DWD • New reference atmosphere - motivation • The existing reference atmopshere, which is based on the assumption , has the inconvenient property that dT0/dz gets increasingly negative in the stratosphere • This severely limits the allowable vertical extent of the model domain; for the default values used in COSMO, T0 reaches 0 K at a height of 28.9 km • Another physically questionable property is that the reference pressure is still nonzero ( 1.05 hPa) where T0 = 0 K

  4. Günther Zängl, DWD • New reference atmosphere - definition • The new reference atmosphere is based on • This expression also allows for an analytical integration of the hydrostatic equation, yielding • and • Present default values: T00 = 213.15 K, ΔT = 75 K, H = 10 km

  5. Günther Zängl, DWD • New reference atmosphere (cont’d) • As the new reference profile approaches an isothermal stratosphere, there is no longer a limit to the vertical extent of the model domain (and it is much closer to reality) • In the context of implementing the new reference atmosphere, an inconsistency in the calculation of the reference pressure at full levels was discovered: it is taken to be the arithmetic mean of the adjacent half levels, but this is also done for geopotential height in the RK core • Instead, we now use either the analytical formula or integrate the hydrostatic equation to get the full-level reference pressure

  6. Günther Zängl, DWD • Test program • Selected cases: 03/03/2008, 30/05/2008 (each +72h) • Leapfrog core (operational configuration) • Runge-Kutta core (standard implementation) • RK core using discretized hydrostatic equation to compute full-level reference pressure • RK core using analytical formula to compute full-level reference pressure • RK core with new reference atmosphere, combined with both consistent methods to compute reference pressure • Unapproximated pressure tendency equation (L. Torrisi) • Generally: Initialization from GME assimilation run (cold start), lateral boundary conditions from operational GME forecast

  7. Günther Zängl, DWD COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 12h Sea-level pressure Pressure difference forecast-analysis

  8. Günther Zängl, DWD COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 24h Sea-level pressure Pressure difference forecast-analysis

  9. Günther Zängl, DWD COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 36h Sea-level pressure Pressure difference forecast-analysis

  10. Günther Zängl, DWD COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 48h Sea-level pressure Pressure difference forecast-analysis

  11. Günther Zängl, DWD COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 60h Sea-level pressure Pressure difference forecast-analysis

  12. Günther Zängl, DWD COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 72h Sea-level pressure Pressure difference forecast-analysis

  13. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 12h Runge-Kutta Leapfrog

  14. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 24h Runge-Kutta Leapfrog

  15. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 36h Runge-Kutta Leapfrog

  16. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 48h Runge-Kutta Leapfrog

  17. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 60h Runge-Kutta Leapfrog

  18. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 72h Runge-Kutta Leapfrog

  19. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 12h Runge-Kutta new Leapfrog

  20. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 24h Runge-Kutta new Leapfrog

  21. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 36h Runge-Kutta new Leapfrog

  22. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 48h Runge-Kutta new Leapfrog

  23. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 60h Runge-Kutta new Leapfrog

  24. Günther Zängl, DWD Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 72h Runge-Kutta new Leapfrog

  25. Günther Zängl, DWD Temporal evolution of pressure bias, case 1 (3/3/08)

  26. Günther Zängl, DWD RMS error (after bias removal), case 1 (3/3/08)

  27. Günther Zängl, DWD Temporal evolution of pressure bias, case 2 (30/5/08)

  28. Günther Zängl, DWD RMS error (after bias removal), case 2 (30/5/08)

  29. Günther Zängl, DWD • Summary of test results • The new reference atmosphere tends to improve the pressure forecast; in both cases, the results are similar to those obtained with the old leapfrog core • The way of computing the reference pressure (analytical / numerical integration of the hydrostatic equation) has a marked systematic impact on the pressure bias • The unapproximated pressure tendency equation affects the temporal evolution of the pressure bias; however, more tests are needed for quality assessment • Tests (not shown here) with higher model top (28 instead of 22 km) do not indicate a systematic impact

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