Application of multigrid NLS-4DVar in radar radial velocity data assimilation with WRF-ARW

Figures & data

Figure 1. Vertical profiles of the RMSEs of (a) $u$ (zonal) wind (m s⁻¹), (b) $v$ (meridional) wind (m s⁻¹), (c) temperature (°C), and (d) water vapor mixing ratio (g kg⁻¹) from CTRL, nonlinear least-squares (NLS) assimilation with $I_{max}=3$, and multigrid NLS (MG_NLS) with $n=3$ results at the analysis time.

Figure 2. RMSEs of the 24-h forecast of accumulated rainfall (from 0000 UTC 8 August to 0000 UTC 9 August) with the initial condition from CTRL, nonlinear least squares (NLS) assimilation with $I_{max}=3$, and multigrid NLS (MG_NLS) with $n=3$ methods.

Figure 3. RMSEs of 24-h forecast of accumulated rainfall (from 0000 UTC 8 August to 0000 UTC 9 August) with the initial condition from the CTRL, nonlinear least squares (NLS₁), and multigrid NLS (MG_NLS_i) ($\mathrm{i}=2,3$ represents the total number of grid levels) methods.

Table 1. CPU time of each grid level and total time for NLS₁ and MG_NLS_i ($i=2,3$, where $\mathrm{i}$ represents the number of grid levels) (units: s).

Method	NLS1	MG_NLS2	MG_NLS3
65 × 55	0	0	62.729 + 60
130 × 110	0	118.916 + 60	112.735 + 60
260 × 220	300.368	305.041	305.994
Total time (s)	300.368	483.958	601.459

Figure 4. RMSEs of the 24-h forecast of accumulated rainfall (from 0000 UTC 8 August to 0000 UTC 9 August) with the initial condition from CTRL and multigrid nonlinear least-squares assimilation (MG_NLS) ($n=3$) with different localization radii.