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a
0.8
0.6
dy
TL
0.4
dy
NL
0.2
0.0
critical cloud water
−
0.2
10
−
6
10
−
5
10
−
4
10
−
3
10
−
2
cloud water mixing ratio (kg
kg
−
1
)
dx
b
0.8
0.6
dy
TL
dy
TL2
0.4
dy
NL
0.2
0.0
Power=2.0
critical cloud water
Power=1.0
−
0.2
10
−
6
10
−
5
10
−
4
10
−
3
10
−
2
cloud water mixing ratio (kg
kg
−
1
)
dx
Fig. 11.1
Autoconversion function of cloud water into precipitation (
black solid line
) based on
Sundqvist et al.
(
1989
). A change in the cloud water,
dx
, results in a change of precipitation,
dy
NL
, in the case of non-linear (NL) model.
dy
TL
is the corresponding change in precipitation
given by the tangent-linear (TL) model. (
b
) Describes the modified function which is less steep
and helps to reduce the TL increments to
dy
TL
2
(closer to
dy
NL
)
1. Simplified non-linear forward model design, coding, tuning and validation.
2. Tangent-linear coding and testing.
3. Adjoint coding and testing.
4. Performance assessment in data assimilation and other applications (see exam-
ples in Sect.
11.6
).
11.4.1
Simplified Non-linear Version
In the first stage, the non-linear version of the new simplified physical parametriza-
tion needs to be designed. This can be achieved through either an “upward” or
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