overview motivation of the new reference atmosphere and description

15.09.2008 Günther Zängl, DWD 1

A new reference atmosphere for the COSMO model

Günther Zängl

Deutscher Wetterdienst, Offenbach, Germany

15.09.2008 Günther Zängl, DWD 2

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)

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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

10

lnc

pd

dT

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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

H

zTTzT exp)( 000

TT

TTH

z

TR

gHpzp

d 00

00

00000

explnexp)(

TTTp

p

gH

TR

TTTpT

d

)(lnexp

)(

0000

000

000000

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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

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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

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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

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Sea-level pressure Pressure difference forecast-analysis

COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 24h

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Sea-level pressure Pressure difference forecast-analysis

COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 36h

15.09.2008 Günther Zängl, DWD 10

Sea-level pressure Pressure difference forecast-analysis

COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 48h

15.09.2008 Günther Zängl, DWD 11

Sea-level pressure Pressure difference forecast-analysis

COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 60h

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Sea-level pressure Pressure difference forecast-analysis

COSMO-EU „cold start“ forecast initialized at 00 UTC 03/03/2008, operational setup, validation against GME assimilation run t + 72h

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Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 12h

Runge-Kutta Leapfrog

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Runge-Kutta Leapfrog

Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 24h

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Runge-Kutta Leapfrog

Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 36h

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Runge-Kutta Leapfrog

Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 48h

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Runge-Kutta Leapfrog

Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 60h

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Runge-Kutta Leapfrog

Comparison between reference run (operational setup; right) and experiment with (unmodified) RK core t + 72h

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Runge-Kutta new Leapfrog

Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 12h

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LeapfrogRunge-Kutta new

Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 24h

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LeapfrogRunge-Kutta new

Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 36h

15.09.2008 Günther Zängl, DWD 22

LeapfrogRunge-Kutta new

Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 48h

15.09.2008 Günther Zängl, DWD 23

LeapfrogRunge-Kutta new

Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 60h

15.09.2008 Günther Zängl, DWD 24

LeapfrogRunge-Kutta new

Comparison between reference run (operational setup; right) and experiment with RK core and new reference atmosphere (discrete hydrost. eqn.) t + 72h

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Temporal evolution of pressure bias, case 1 (3/3/08)

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RMS error (after bias removal), case 1 (3/3/08)

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Temporal evolution of pressure bias, case 2 (30/5/08)

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RMS error (after bias removal), case 2 (30/5/08)

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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