Digital Signal Processing Reference
In-Depth Information
Note that when the water vapor is non-negligible in the lower altitudes, the
temperature derived from Eq. (
6.5
) is generally called dry temperature, which will
be colder than the real temperature. In addition, given the density and pressure
profiles as a function of geometric height (or absolute altitude), the geopotential
heights of constant pressure levels can also be derived. As RO provides independent
values of pressure and height, the geopotential height at a constant pressure level
from RO can be retrieved only based on the density profile above the level of interest
(Leroy
1997
). Such derivation will therefore have the advantage of not relying on
the surface pressure and temperature measurements that are generally required for
conventional geopotential heights calculation.
6.1.3
Moist Atmosphere Retrieval
When the water vapor becomes significant in the middle and lower troposphere,
derivation of water vapor, temperature and pressure from refractivity measurement
becomes under-determined. It requires independent knowledge of one of the three
parameters (
T
,
P
or
P
w
) in order to solve for the other two parameters. Combining
Eq. (
6.1
) and the ideal gas law, the density can be expressed as
N.r/
;
m
v
c
1
R
c
2
P
w
.r/
T
2
.r/
.r/
D
(6.6)
where
m
v
is the mean molecular mass of moist air. And the Eq. (
6.1
) can be
rearranged to solve for water vapor:
P
w
.r/
D
N.r/T
2
.r/
c
1
P.r/T.r/
=c
2
:
(6.7)
or solve for temperature given a-priori water vapor after simple iteration
c
1
P.r/
N.r/
c
2
P
w
.r/
T.r/
T.r/
D
C
:
(6.8)
Due to the large water vapor variation and the lacking of observational constraint
in models, the water vapor uncertainty generally far exceeds the pressure and
temperature uncertainties. Therefore given the precise measurement of refractivity
from GNSS RO as well as the independent knowledge of temperature (e.g., from
in-situ observations, global model analysis and reanalysis or climatology), the
water vapor pressure can be derived iteratively from Eqs. (
6.4
,
6.5
,
6.6
and
6.7
).
While the approach is relatively simple, the RO water vapor retrieval (given the
a-priori temperature) or temperature retrieval (given the a-priori humidity) will
contain measurement error in RO refractivity and uncertainties in the a-priori
information.
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