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Numerical experimentation with regional atmospheric models

Hans von Storch and Ralf Weisse

8IMSC, Lüneburg, 15. March 2001

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The Rinke & Dethloff study on regional modelling of the Arctic atmosphere

Rinke, A., and K. Dethloff, 2000: On the sensitivity of a regional Arctic climate model to initial and boundary conditions. Clim. Res. 14, 101-113.

Ensemble standard deviation 500 hPa height [m²/s²]

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Thus, the development in the interior of the limited domain is only partially controlled by the lateral boundary conditions.

Instead, the nonlinear chaotic processes acting on all spatial scales have a marked impact on the development. Small disturbances, be they in the initial conditions, lateral boundary conditions, or in the parameterizations introduce the potential of divergent evolution at any time.

The stronger the influence of the large-scale state, the smaller the potential for divergence (spectral nudging, smaller area).

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Not only in global GCMs but also in regional GCMs variations unrelated to external causes (noise) are formed.

The assessment of a paired model experiment, in which the effect of a treatment is studied, needs the discrimination between the effect of the treatment (signal) and noise.

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Chervin/Schneider test concept.

Thus, to discriminate between the effect of a treatment (signal) and variations due to internal chaotic dynamics (noise), the signal-to-noise ratio needs to be determined.

If the signal-to-noise ratio is larger than a critical value, to be rarely expected under the null hypothesis of a zero signal, then the null hypothesis is rejected, and the evidence is considered sufficient to accept the alternative hypothesis, namely that the treatment has really an effect.

Chervin, R.M. and S.H. Schneider, 1976: On determining the statistical significance of climate experiments with general circulation models. J. Atmos. Sci., 33, 405-412

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Do do so, N realisations of the control (y) and of the anomaly (x) are averaged, and the t-ratio is computed

With the estimated standard deviation

When the difference is actually zero (null hypothesis), then T is t-distributed with N-2 degrees of freedom. Thus, the null hypothesis may be rejected with a risk of less than 5% if T > 2.23 (when N=6 as in the following).

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Example: The case of the relevance of the sea state on the atmospheric variability

Hypothesis: The dynamical state of the ocean waves (specifically the shape of the spectra, or age) affect in a physically significant way the state of the overlying atmosphere (Janssen). Growing (young) waves suck momentum from the wind field, thereby damping the formation of storms.

Weisse, R., H. Heyen and H. von Storch, 2000: Sensitivity of a regional atmospheric model to a sea state dependent roughness and the need of ensemble calculations. Mon. Wea. Rev. 128: 3631-3642

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Experimental design: Regional atmospheric model (HIRLAM) covering the North Atlantic.

Control: roughness of sea surface parameterized by the Charnock formula.

Anomaly: roughness of sea surface determined from wave spectra simulated interactively with wave model WAM.

In each configuration one full year was simulated (conventional setup.)

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HIRLAM computation domain, covering the North Atlantic storm track, where wind-wave interaction is maximum.

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1 year simulation (January – December 1993), SLP

Area average of rms difference between control (Charnock) and experiment (interactive WAM model)

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control (Charnock) experiment (WAM) difference

January episode with large differences

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Additionally, another 20 months were simulated with HIRLAM.

For each configuration, control (Charnock) and anomaly (WAM model coupled), 5 Januaries and 5 Junes were simulated. They differed only with respect to the initial state, which was taken from the year-long simulation one day apart (e.g. 2, 3, 4, 5 and 6 January).

Thus for the basic experiment, two ensembles of 6 „control“ and „anomaly“ members each were available to assess the internal variability (noise) and the systematic difference (signal).

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Area averaged rms of the six control simulations, relative to their joint spatial average (solid)and of the six anomaly simulations relative to their joint spatial average (dashed).

Note that the rms is calculated for each time separately – the noise is not stationary but time dependent.

SLP

January

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Differences between members of the „control ensemble“

13. Jan

14. Jan

15. Jan

#3 - #1 #6 - #1 #6-#3

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Rms of members of the anomaly ensemble (interactive WAM model) compared to control ensemble variations.For both ensembles, the rms is calculated relative to the control average.

The gray band is the estimated 95% „confidence“ interval of rms within the control ensemble. 95% of all states consistent with the control should be within the band. About 40% of the anomaly rms’s (dotted) curve are outside the band. Mostly after 19. January, when the variability is small!

Rms relative to control mean; SLP in January

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Result of t-test for rms (red). The black interval represents the 95% critical values, so that the interactive WAM model is found to be associated with statistically significant large rms’s unlikely to be found in the control setup.

A is a situation with an insignificant difference, B a situation with a significant difference.

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A: Large differences and large noise, thus inclusive result.

Ensemble mean differences in SLP [hPa]

Points with significant t-statistics are in blue.

Six anomaly (interactive WAM; solid) and six control

simulations (Charnock; dashed) of 500 hPa height [gpm]

15. Jan, 0 UTC

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B: Small differences but statistically significant. Evidence for physically insignificant treatment.

Ensemble mean differences in SLP [hPa]

Points with significant t-statistics are in blue.

Six anomaly (interactive WAM; solid) and six control simulations

(Charnock; dashed) of 500 hPa height [gpm]

29. Jan, 0 UTC

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Conclusions

(1) Also in regional climate models internal variability is formed; only part of the variability is related to varying boundary forcing.

(2) The internal variability may be suppressed by a sufficiently small area, or by spectral nudging (not shown)

(3) Numerical experiments with RCMs need to discriminate between noise and signal, like in global GCM experiments.

(4) The noise in RCMs is not stationary so that its statistics can hardly be extracted from extended simulations; instead sufficiently large ensembles are needed.

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Growing wind waves have an effect on the atmospheric flow, but the effect is small in dynamically active times, and can be detected only in calm situations. Thus, the effect is physically insignificant, and the use of the computationally much less demanding Charnock formula is to be preferred.The effect on the simulation of the wave field may be benign, though.

Is this result of interest?

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Reserveabbildungen

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Development of 500 hPa height at one point in the interior in the four ensemble runs