Background Error Correlation Modeling with Diffusion Operators - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 191

118 ° E 120 ° E 122 ° E 1 24 ° E 12 6 ° E 1 2 8 ° E 13 0 ° E 1 32 ° E

35

30

28 ° N 25

20

15

26 ° N

10

24 ° N

22 ° N

20 ° N

18 ° N

Fig. 8.7 Diagonal elements of B g in the Okinawa region at z D 20 m. The actual values are

multiplied by 10 4

8.3.5 LH Experiments in 3d Setting

To check the performance of the LH0 and LH1 methods further, a larger 3d NCOM
domain is set up in the Okinawa region (Fig. 8.7 ) with horizontal resolution of 10 km
and 45 vertical levels. The state vector dimension

N (total number of the grid points)

in this setting was 862,992.
Because of the large , it is computationally unfeasible to directly compute all

the diagonal elements of the BEC matrix. Therefore, accuracy checks are performed
on a subset of 10,000 points, randomly distributed over the domain and the value of
h " i is estimated by averaging over these points.
The diffusion tensor is constructed in the same way that is described in
Sect. 8.3.1 , but the generating field u

N

. x / is taken to be the horizontal velocity field

from an NCOM run. The value of 3 (in the vertical direction) is independent of

horizontal coordinates, but varies in the vertical as ı z is the vertical

grid step. Figure 8.7 illustrates spatial variability of the B g diagonal elements at
z

3ı z ,where

m. The smallest values are observed in the regions of the Kuroshio and
the Nor th E quatorial Current, where the largest velocities are observed, and the
˝ D

D 20

p det

reaches its largest values ( 8.44 ). To better test the algorithm, a relatively
small threshold value of v D 0:02 m/s is prescribed, so that diffusion is anisotropic

in more than 90 % of the grid points.