The Advances in Targeted Observations for Tropical Cyclone Prediction Based on Conditional Nonlinear Optimal Perturbation (CNOP) Method - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 571

Forecasting (WRF) model have been used to assimilate the operational Dropsonde
Observations for Typhoon Surveillance near the Taiwan Region (DOTSTAR) in the
conduction of observation system experiments (OSEs). Except for clarification, the
model horizontal resolution is 60 km and there are 11 vertical levels in the following
studies.
In this chapter, when the FSV is considered, it will be obtained by solving the
( 24.8 )and( 24.9 ). Thus both CNOP and FSV can be obtained by using the same
optimization algorithm to facilitate comparison, and the optimization algorithm
employed is the spectral projected gradient 2 (SPG2) ( Birgin et al. 2001 ), which
calculates the least value of a function of several variables subject to box or
ball constraints. The cost function implemented for the calculation is J 1 .ı X 0 / D

X T
0

J.ı . The gradient

of the cost function with respect to the initial perturbation is required for the SPG2
algorithm, and the adjoint model of MM5 is used to efficiently calculate the gradient.
When other SVs have been considered, the SVs would be obtained by using the
Lanczos algorithm ( Ehrendorfer and Errico 1995 ).
For simplicity we choose C 1 D C 2 D C ,and C represents the metric of total dry
energy, in a continuous expression:

X 0 / , with the same initial constraint condition ı C 1 ı X 0 ˇ

" u 0 2

2 # dzdD

Z Z 1 p s 0

p r

X 0 / D 1
D

C c p
T r

T C

C v 0 2 T 0 2

. •

X 0 /

. •

C R a T r (24.10)

D 0

where R a are the specific heat at constant pressure and the gas con-

stant of dry air respectively (with numerical values of

c p and

Jkg 1 K 1 and

1005:7

Jkg 1 K 1 / 287:04 . The reference parameters are the following: T r D 270 K,

p s 0 , which are components of the state vector, are
the perturbed zonal and meridional wind components, temperature, and surface
pressure respectively. The integration extends over the full domain D and the vertical
direction z .

hPa. u 0 ; v 0 ; T 0 ;

p r D 1;000

24.3 Properties of the CNOP Sensitive Areas

24.3.1 Definition of Sensitive Areas and Calculation

of Similarity

For CNOP and FSV, the sensitive area is defined as the horizontal grid points where
the function f.i;j/ exceeds a specified threshold value c . The function f.i;j/ is a

vertically-integrated total dry energy function

Z 1
0 E d .i;j;

f.i;j/ D z / dz (24.11)