Table 1
Comparison of large-scale blending methods. The second column shows the timing of the blending step (before, after, or as simultaneous with the analysis step).
| METHOD | TIMING | FLOW-DEPENDENT DA/LSB | REFERENCES |
|---|---|---|---|
| ALSB | after | possible/no | Yang (2005), Caron (2013), Wang et al. (2014b), Wang et al. (2014a), Hsiao et al. (2015), Zhang et al. (2015) |
| BLSB | before | possible/no | Bučánek and Brožková (2017), Milan et al. (2023), Gainford et al. (2024) |
| nested 3DVar | simultaneous | no/no | Guidard and Fischer (2008), Dahlgren and Gustafsson (2012), Vendrasco et al. (2016), Keresturi et al. (2019) |
| nested EnVar | simultaneous | yes/yes | our study |
Figure 1
Time development of analysis RMSEs in the (a) 3DVar and (b) EnVar experiments with uniform observations. The values on the legend indicate time-averaged RMSEs. The dotted lines at RMSE = 1 indicate the standard deviation of the observation error, (c, d) as in (a, b), but for the differences from LAM DA for (c) 3DVar and (d) EnVar experiments.
Table 2
Skill scores of the analysis MSE and contributions of different scales in the experiments with uniform observations. Values in parentheses indicate the MSEs of No LAM DA.
| METHOD (MSEref) | ALL k (1.51e-01) | k ≤ 24 (9.87e-02) | k > 24 (5.22e-02) |
|---|---|---|---|
| 3DVar | –1.4 | –1.6 | 0.18 |
| BLSB+3DVar | –0.10 | –0.38 | 0.27 |
| Nested 3DVar | 0.052 | –0.22 | 0.27 |
| EnVar | 0.085 | –0.21 | 0.29 |
| BLSB+EnVar | 0.28 | –0.014 | 0.29 |
| Nested EnVar | 0.20 | –0.073 | 0.27 |
Figure 2
Time averaged analysis errors in state space: results of (a) 3DVar and (b) EnVar experiments with uniform observations. The dashed curves in (b) show the time averaged analysis spreads in each experiment. Observational frequency in LAM experiments is shown below each figure.
Figure 3
Time averaged analysis errors in spectral space: results of (a) 3DVar and (b) EnVar experiments with uniform observations. The bottom and top axes indicate the wavenumber and wavelength defined in the global domain, respectively. The vertical magenta lines indicate the truncation wavenumber in the LSB experiments.
Figure 4
RMSE of deterministic forecasts from the (a) 3DVar and (b) EnVar experiments with uniform observations. Each curve is averaged over the assimilation cycles. Circles indicate a significant improvement over downscaling (p < 0.05). Thicker gray curves show the forecast RMSEs of the GM within the LAM domain. Horizontal axes indicate hours from the analysis time.
Table 3
Time averaged analysis RMSEs in the experiments with dense and uneven observations.
| METHOD | EXP. 2 | EXP. 3 | EXP. 4 | EXP. 5 |
|---|---|---|---|---|
| 3DVar | 3.29 | 1.33 | 3.34 | 0.652 |
| BLSB+3DVar | 0.331 | 0.327 | 0.328 | 0.329 |
| Nested 3DVar | 0.323 | 0.313 | 0.323 | 0.311 |
| EnVar | 0.662 | 0.371 | 0.543 | 0.315 |
| BLSB+EnVar | 0.295 | 0.285 | 0.291 | 0.283 |
| Nested EnVar | 0.287 | 0.273 | 0.307 | 0.258 |
Table 4
As for Table 2, but in the experiments with dense and uneven observations moving in the LAM domain (Exp. 5).
| METHOD | ALL k | k ≤ 24 | k > 24 |
|---|---|---|---|
| 3DVar | –4.7 | –4.5 | –0.17 |
| BLSB+3DVar | 0.086 | –0.19 | 0.27 |
| Nested 3DVar | 0.13 | –0.15 | 0.27 |
| EnVar | 0.15 | –0.15 | 0.29 |
| BLSB+EnVar | 0.30 | 0.014 | 0.29 |
| Nested EnVar | 0.40 | 0.11 | 0.29 |
Figure 5
As for Figure 1b, d, but obtained in experiments with dense, mobile observations.
Figure 6
As for (a) Figure 2b and (b) Figure 3b, but obtained in experiments with dense, mobile observations.
Figure 7
As for Figure 4, but obtained in experiments with dense, mobile observations.