Modeling the GABLS4 strongly-stable boundary layer with a GCM parameterization: parametric sensitivity or intrinsic limits?

o te d on 2 N ov 2 2 — C C -B Y 4. 0 — h tt p s: / d o .o rg /1 0 1 0 / ss o r. 1 50 3 9 .1 — T h is a p re p ri n t a d h a n o b ee n p ee r re v ie w ed . D a a m ay b e p re li m in a y. Modeling the GABLS4 strongly-stable boundary layer with a GCM parameterization: parametric sensitivity or intrinsic limits? Olivier Audouin, Romain Roehrig, Fleur Couvreux, and Danny Williamson CNRM, 9 University of Toulouse, Meteo-France, CNRS CNRM, Université de Toulouse, Météo-France, CNRS Université Toulouse, CNRM, Meteo-France, CNRS University of Exeter

nocturnal strong SBL observed at Dome C, Antarctic Plateau, is used. The standard cal-23 ibration of the ARPEGE-Climat 6.3 turbulence parameterization leads to a too deep SBL, 24 a too high low-level jet and misses the nocturnal wind rotation. This behavior is found 25 for low and high vertical resolution model configurations. The statistical tool then proves 26 that these model deficiencies reflect a poor parameterization calibration rather than in-27 trinsic limits of the parameterization formulation itself. In particular, the role of two lower 28 bounds that were heuristically introduced during the parameterization implementation 29 to increase mixing in the free troposphere and to avoid runaway cooling in snow-or ice-30 covered region is emphasized. The statistical tool identifies the space of the parameter-31 ization free parameters compatible with the LES reference, accounting for the various 32 sources of uncertainty. This space is non-empty, thus proving that the ARPEGE-Climat   The focus is here on its turbulence parameterization, which is based on the work of Cuxart where α ψ and CM are free parameters of the parameterization, L m is the mixing length, 198 and φ ψ is a stability function. φ ψ is taken to 1 for momentum and turbulence kinetic 199 energy (ψ ∈ {u, v, e}). For the potential temperature θ, the following formulation is used: where C is a free parameter.
In Equation 1, CM modulates all turbulent fluxes in the same way. α u and α v are taken 201 to 1, and α θ is the inverse Prandtl number in neutral condition (i.e. when φ θ = 1). In 202 the following, α e and α θ will be referred to as AE and AT, respectively.

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Eddy diffusivity coefficients K ψ depend on the intensity of e. The time evolution 204 of e is given by: where ρ is the air density, g is the gravity acceleration, and L the dissipation length.

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L is assumed to be proportional to the mixing length: L = CEL m , with CE a free In case of shallow stable boundary layer, another lower bound, which applies mainly 217 close to the surface, is introduced directly on the turbulent fluxes, to avoid runaway cool-218 ing of the surface (especially in snow-or ice-covered regions): where KOZMIN and ZMAX are two free parameters, and ∆ψ is the vertical differ-  The friction velocity u * is computed following Paulson (1970): where U 1 is the wind intensity (U 1 = u 2 1 + v 2 1 ) at the first model level of altitude z 1 , where θ 1 and θ s are the potential temperature at the first model level and at the sur- and Noilhan and Mahfouf (1996) read: and are used to compute the surface fluxes: where C p is the heat capacity of air at constant pressure.

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Note that the present surface flux parameterizations include internal free param-258 eters (B 1 = 10, B 2 = 5, B 3 = 15), which are not considered in the following analysis. cept very close to the surface. In particular, they are substantial differences for the sur-

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We also explore the turbulence parameterization behavior for two different verti-    process has thus converged and it is not necessary to perform additional waves.

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The convergence questionis discussed in section 6.2.

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At 0100 LT, a low-level jet is well formed in all the LES (Fig. 1f). The altitude of its 437 peak is similar in all LES, around 22 m, and its intensity ranges between 5 and 6 ms −1 .

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The inertial rotation of the wind at 25 m is further emphasized in Fig to as θ 2m and θ 8m respectively); these two vertical levels allow to constrain the θ ver-455 tical gradient. These two metrics are computed at 0300 LT, when θ is minimum in the 456 LES. The low-level jet structure is measured using the maximum of the supergeostrophic 457 wind speed and the wind speed at 55 m (referred to as jet MAX and w 55m respectively).

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The latter altitude corresponds to the level where the wind returns to its geostrophic value  It will also be discussed in 6.2.

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The metric values, computed for each simulation of this Wave 1, are used as a train- reduce the turbulent mixing.   Table 2). From

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Wave 4, jet MAX , w 55m and the one on θ 8m are no longer discriminating, i.e. for these met-

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Grey color means that this density is close to zero, given the color scale used for the plot.

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The closer the color to yellow, the greater the density, thus indicating that this combi-    Table 3 shows the evolution of the met-598 rics for eight waves. From Wave 3, the results are already satisfying for most of the met-599 rics. Only θ 55m needs a few more waves to achieve reasonable values. The remaining (NROY) 600 space is finally slightly more than 0.1% of the initial space (Fig. 3b).

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The θ vertical profiles at 0300 LT of all the Wave 9 simulations are very close to 602 the LES (Fig. 4b, blue lines). The time evolution of the 8-m potential temperature still 603 presents some dispersion, which is consistent with the LES uncertainty. Wave 9 simu-604 lations also capture well the sharpened wind speed vertical structure at 0100 LT, and 605 much better than CM6-LR (red line). There is still some significant spread in the jet in-606 tensity, but again, it reflects the LES discrepancies (Fig. 4e). All the simulations repro-607 duce well the 25 m wind rotation (Fig. 4d). The iterative refocussing approach is now applied to a less constrained configura-  The iterative refocussing applied on the present configuration makes use of the same 638 four metrics as for CM6-LR-SHF. Table 4  to identify the main model biases (and especially those we care about) and then to de-676 sign the appropriate metrics to quantify them. We have already seen in Section 5.2 that 677 the two main identified biases are a weak nocturnal cooling and an insufficiently marked 678 low-level jet structure. Analysis of the potential temperature profile at 0300 LT (Fig. 4b),  The third feature can be captured by the wind intensity at the third model level (w 55m ).  Table 5. The w 29m metric is much less discriminating than the other three.

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18% of the original space is compatible with the reference after 9 waves, as opposed to 707 around 0.5 to 1% for the other metrics. The LES uncertainty for this metric explains part 708 of this result. The importance of the reference uncertainty relative to the bias is quan-709 tified as the ratio between the two quantities (Table 5). It is thus shown that consider- give indications about the discriminatory ability of a given metric.  space no longer decreases as we perform more waves (e.g., Table 6). Using the SCM-LR-764 SHF experiment, we illustrate here the NROY convergence and analyze the evolution 765 of the different uncertainty sources that we need to take into account to monitor this con-766 vergence.

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In the SCM-LR-SHF experiment, the NROY space size has converged from about 768 the fourth wave. The NROY space estimated at the end of Wave N is defined using the   have an implausibility lower than 3 (the chosen cutoff, cf. Section 4) despite the reduced 776 emulator uncertainty within the NROY space compared to the previous wave.

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As the NROY space size reduces during the successive waves, the 70 SCM runs sam-778 ple a much smaller space, thus leading to improved surrogate models within the NROY 779 space, with reduced uncertainty. This is particularly the case for the metrics θ 55m and 780 w 55m , for which from Wave 2-3 the surrogate model uncertainty falls mostly below or 781 is of the same order of magnitude as the reference uncertainty ( Fig. 8f and 8h). For θ 8m 782 the surrogate model uncertainty is also reduced after Wave 1 (Fig. 8e) The different metrics estimated by the emulators also converge rapidly and from 788 Wave 3 (Wave 5 for w 55m ) onwards ( Fig. 8a-d), only a few outliers fall outside the range The analysis of the metric convergence also emphasizes the question of discrepancy.

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If for θ 8m , θ 55m and w 55m , the SCM simulations converge to the mean reference, this is   method and in order to compare results, the structural error σ 2 d,f is taken to zero. This 823 formulation is used to estimate the NROY space, directly from the 10 4 SCM ensemble.

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Note that to appropriately characterize the NROY space, it is necessary that it contains 825 enough points, at least a few hundreds. The NROY space obtained using the four met-826 rics in Section 5.2 is about 0.1% of the initial space. It has been numerically evaluated 827 using the implausibility computed over 10 6 points, so that it contains in the end around 828 10 3 points. With only 10 4 points in the initial space, only an order of 10 points is ex-829 pected to remain, which is clearly not sufficient to fully characterize the NROY and make 830 its estimate not too much sensitive to the input space sampling. This further empha-831 sizes the relevance of using surrogate models, even in this SCM framework. Therefore, 832 the statistical framework is evaluated using only the metric w 29m , as it keeps a sufficient 833 fraction of the initial space, namely about 18% using emulators (thus about 1,800 points).

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In parallel, a NROY space is estimated using the emulators built in 5.2 on the same 10 4 835 points in the parameter space. The use of the same points for both estimates avoids sam-836 pling effects in the comparison.

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In experiments using emulators, the threshold for implausibility is set at 3. This Stable boundary layers are still critical features for weather and climate models.

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In the present work, we seek to assess whether these model deficiencies reflect calibra-  The present work is also the opportunity to gather and formalize our experience