A Weak Constraint 4D-Var Assimilation System for the Navy Coastal Ocean Model Using the Representer Method - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 378

and

ı 2t D . t C t t t /

The NCOM equations are then discretized in flux conservative form as follows

x

u

y

u

.f C C curv / v y x y z u u

u

z u gı x . C atm tp / ı 2t . / D xy z

2t

z u 1

u

x

0 ı x .p i /

z u u a x u x z v v a x u y ı x y

u

ı y x

v

ı z w x u z xy

x u sor C F u

C xy z Q

0
@

1
A

K M x

u u

z w x n C 1 ı z u n C 1

C x y ı z (15.14)

v v

gı y C atm tp

x y

ı 2t . z v v / D xy z .f C C c u r v / u x y x

v

z v

2t

z v 1

v

x

o ı y .p i /

z u u a y v x z v v a x v y ı x y

u

ı y x

v

ı z w y v z xy

y v sor C F v

C xy z Q

0
@

1
A

K M y

v v

z w y n C 1 ı z v n C 1

C x y ı z (15.15)

xy
2t ı 2t . z / D ı x .y

u

z u u a / ı y .x

v

z v v a / ı z .xy w / (15.16)

T/ D ı x

x ı y y xy

2t ı 2t .

u

z u u a T

v

z v v a T

z y x

ı z

z

xy w T

y

ı x T n 1

u

z u

u
H

A

C xy z QT sor C ı x

x

u