Fig. 1
The smoothing property.
Fig. 2
Schedule of grids for (a) V-cycle, (b) W-cycle and (c) FMV-cycle.
Fig. 3
The minimisation procedure of the incremental 3D-Var.
Fig. 4
The horizontal grid structures of WRF. (a) WRF model: Arakawa C-grid staggering, (b) WRF-Var: unstaggered Arakawa A-grid.
Fig. 5
(a) Non-weighted prolongation for CCFD, (b) weighted prolongation for CCFD.
Fig. 6
(a) The observation data, (b) the contour of observation data, (c) the analysis field of 3D-Var with the conjugate gradient method and (d) the analysis field of 3D-Var with the multigrid method.
Table 1. The result of numerical experiment 1
030.62536518030.6253651811.1354160710.0941901520.1242786820.0003846930.0134909130.0000016440.0016098640.0000000150.0002011850.0000000060.0000265970.0000033780.0000004290.00000005100.00000001110.00000000
Fig. 7
(a) The true state of temperature, (b) the contour of true data, (c) the observation data and (d) the contour of observation data.
Fig. 8
(a–c): The analysis fields of 3D-Var with the conjugate gradient method at each iterative step 1(a), 7(b), and 13(c), (d–f): The analysis fields of 3D-Var with the multigrid method at each iterative step 1(d), 3(e) and 5(f).
Table 2. The result of numerical experiment 2
020.43552705020.4355270512.6409575010.0638083020.4188588220.0002616130.0687252030.0000011740.0101991340.0000000150.0017645250.0000000060.0003116970.0000525280.0000078790.00000138100.00000020110.00000003120.00000001130.00000000