Averagingkernelsandtheirusein validatingAIRSozoneretrievals A work - PowerPoint PPT Presentation

Averaging
kernels
and
their
use
in
 validating
AIRS
ozone
retrievals
 A work in progress Bill
Irion
‐
April
16,
2008
 With
thanks
to
Evan
Manning
and
Van
Dang


What’s
an
averaging
kernel?
 The averaging kernel matrix is a measure of how and where the retrieval is sensitive to changes in the “true” state. Retrieved state vector (e.g., an ozone profile) A = ∂ ˆ x ∂ x “True” state vector For AIRS averaging kernel derivation and discussion, see Maddy and Barnet, Vertical resolution estimates in Version 5 of AIRS operational retrievals, submitted to IEEE Trans. Geosci. Remote Sensing , 2007

For
AIRS,
averaging
kernels
are
new
for
 Version
5
retrievals 
 Retrieval determined through perturbing trapezoids m − 1 + T Δ ˆ ˆ m = ˆ ( ) x x α Ozone trapezoids m 0 + T = ˆ ( ) ˆ x α Averaging kernel from AIRS L2 is on the trapezoid grid, not the retrieval grid. A = ∂ ˆ α ∂α So on the trapezoids:

Averaging
kernel
for
ONE
level 
 Sensitivity for 0.1 ozone trapezoid San Cristobal Pressure (mb) centered at 86 mb Stars mark geometric centers of trapezoids Half-width at 1000 0.15 0 half-maximum a ∂ ˆ α / ∂α measure of vertical resolution

Sample
averaging
kernel
for
 all
trapezoids
 0.1 Ozone - San Cristobal Pressure (mb) Geometric mean pressures of trapezoids 1000 0.0 0.6 ∂ ˆ α / ∂α The trace of the Averaging Kernel matrix is the degrees of freedom for the retrieval.

Verticality
 The sum along a row (or column) of an averaging kernel is a rough fraction of how much the result in a trapezoid comes from the spectral data (vs. the a priori .) San Cristobal Averaging Kernel Verticality 0.1 Pressure (mb) 1000 0.0 0.6 0.0 1.0 2.0 ∂ ˆ α / ∂α

Verticality
 The sum along a row (or column) of an averaging kernel is a rough fraction of how much the result in a trapezoid comes from the spectral data (vs. the a priori .) San Cristobal Averaging Kernel Verticality 0.1 Pressure (mb) 1000 0.0 0.6 0.0 1.0 2.0 ∂ ˆ α / ∂α Verticality >> 1 may indicate a problem in damping and trapezoid selection.

Averaging kernel can be placed on the 100-level AIRS support grid by calculating the psuedo-inverse trapezoid matrix: − 1 T T T T = T T T [ ] ′ 100 − level = T A trapezoid T T A ′ ′ 0.1 Pressure (mb) 1000 0.0 0.6 0.0 0.1 ∂ ˆ x / ∂ x ∂ ˆ α / ∂α x = ln(slab column)

Using
Averaging
Kernels
with
correlative
“truth”
 data 
 • Every
retrieval
uses
a
combination
of
observed
data
 and
an
 a
priori
 x est = x 0 + A ( x T − x 0 ) ′ • If
sensitivity
were
perfect,

 A = I ′ • If




were
replaced
by
“truth”
(say,
an
ozonesonde
 x T profile),
then







would
be
a
measure
of
what
the
 x est instrument
should
have
returned
given
its
smoothing
 and
sensitivity.
 • This
assumes
a
linear
regime.


San Cristobal Example
 comparisons
 of
slab
columns
 Churchill Slab Columns (molecules cm -2 )

Procedure
 • Ozone
data
from
WOUDC
(great
stuff!)
 • Slab
columns
calculated
for
ozone
on
AIRS
100‐level
grid
 • AIRS
retrievals
used
to
fill
in
“truth”
above
range
of
sondes
 • Sonde
data
must
at
least
reach
10
mb
 • 3
hr,
50
km
matchup
range

 • “Kerning”
calculation
on
sonde
data
uses
ln(slab
column)
 for
ozone:
 ln x est = ln x 0 + A (ln x T − ln x 0 ) ′

WOUDC
locations


Polar
ozone


Polar
ozone
 A priori missing ozone hole?

Tropical
ozone


Tropical
ozone
 Tropospheric a priori high Tropospheric a priori low

N.
mid‐latitude
ozone


Conclusions
 • Comparison
of
sondes
convolved
with
averaging
 kernel
with
retrievals
generally
indicate
 agreement
within
~20%
in
the
extra‐tropics
 – but
retrieval
can
often
not
recover
from
poor
first
 guess.
 • Further
work
needed
to
understand
high
(>>1)
 verticalities
 – Change
trapezoids
and
damping?
 • Ozone
comparison
indicates
large
departures
 from
zonal
means
affecting
retrieval
 – Final
result
sometimes
worse
than
1st
guess
 – work
on
regional
a
prioris?