Figure 3: Abundance-to-noise ratio and degree of freedom from
the synergy and the single spectral domain retrievals. Dataset is
limited to those retrievals which satisfy the criteria of a reduced
χ2 equal to or smaller than 4 and an ANR equal to or
larger than 1 in MY 27. Top panel: ANR for the synergy, PFS and SPICAM
retrievals. Bottom panel: DOF for the synergy, PFS and SPICAM
retrievals. Data points are layered, with the synergistic points at the
bottom. Solid lines represent averages binned in intervals of 2° Ls.
The ANR values are shown as scattered dots for each individual
retrieval, and the solid curves represent binned averages of 2° Ls. The
selected data are limited to all retrievals with ANR >=1 to
ensure the presence of water vapor. The synergy and SPICAM have very
similar ANR distributions, both averaging at around ANR=5, with the
synergy only occasionally outperforming SPICAM mostly at mid latitudes,
showing that the synergy provides highly robust column abundances.
PFS/TIR displays the smallest spread in ANR, covering the range from
~1.5-6 and with an average of around 4. SPICAM/NIR
retrievals mostly range between 2 and 8 and remain above 4 for all
latitudes north of -40°N.
The DOFs for each method is shown in the bottom panel of Figure 3, where
the notable increase in DOF for the synergy verifies that the water
content along the vertical can be roughly resolved. The DOF fluctuates
around 1.0 for the NIR and TIR single spectral domain retrievals, while
it typically exceeds 1.25 for the synergy, fluctuating around 1.5. Note
that the spread in DOF values is small for NIR compared to TIR, and that
NIR regularly achieves DOFs around 1.5, higher than what is ever
obtained with TIR. In the southern hemisphere and near the north pole,
the TIR DOFs nearly never exceed 1, while the synergy remains stable and
high in the north polar region especially, but also performs reasonably
well in the south. With a DOF consistently higher than one, the synergy
is capable of providing information on the shape of the profile, and a
vertical partitioning can be obtained.
The synergy returns a column abundance and a vertical profile for each
co-located observation. To ensure the synergy is not simply reproducing
the prior when retrieving a vertical profile and to demonstrate that the
synergy is capable of distinguishing near-surface water vapor from the
rest of the column, we quantified the amount of synergistically added
information, compared to the MCD prior, by altitude as a function of
latitude and season. The ratio of the posterior-to-prior errors are
visualized in Figure 4, where each panel represents an altitude
indicated by the number on the left y-axis. Within each panel, data is
binned by 2° in Ls and 2° in latitude. At higher altitudes, the error
ratio is fairly close to one, meaning that the synergy brings little
added information. However, deeper in the atmosphere, more information
is progressively added by the synergy. The panels representing the
atmosphere at 2.5-7.5 km are the altitude regions where most information
is injected, and which benefits the most from the synergistic approach
as was also evident from the single example in Figure 1. The retrieved
profiles could be deviating from the MCD, which we will investigate
further in Section 4.2, but the water mixing ratios are significantly
more constrained, as also demonstrated in Figure 1.
In order to only select retrievals which are robust enough to justify a
deeper analysis, and with a high enough quality that information on the
vertical water distribution can be extracted, four criteria were
established which the retained samples would have to comply with
simultaneously: i) an ANR equal to or larger than 3, ii) a DOF for water
vapor equal to or larger than 1.25, iii) a posterior-to-prior error
ratio equal to or smaller than 0.9 for water volume mixing ratio at 2.5
km (Error ratio), iv) a reduced χ2 of the retrieval
(Chi2) equal to or smaller than 4. Many criteria limits were explored to
optimize the returned number of retrievals versus the quality of said
retrievals. The limits of these criteria can also be tailored for a
specific purpose; the DOF limit was reduced to 1 for the assembly of a
composite column abundance climatology.
A visualization of the statistical distribution of the relative numbers
(per 10 000) and combinations of fulfilled criteria is shown in Figure
5. The first panel of Figure 5 shows the distribution of fulfilled
criteria when the synergistic retrieval method is used. The second and
third panels visualize the relative numbers and distributions of
fulfilled criteria when only the NIR and TIR spectral intervals are
utilized.