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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, D20310, doi:10.1029/2005JD006943, 2006
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Estimating the impact of small-scale variability in satellite
measurement validation
L. C. Sparling,1 J. C. Wei,2 and L. M. Avallone3
Received 1 December 2005; revised 12 March 2006; accepted 27 June 2006; published 27 October 2006.
[1] The necessity of validating satellite measurements of atmospheric chemical
constituents with supplementary in situ measurements leads to problems with
interpretation of the inevitable differences that arise because of measurement resolution or
imperfect collocation, especially for highly heterogeneous fields. In this paper
the contribution of small-scale structure to measurement differences is estimated from
high-resolution aircraft measurements of atmospheric trace gases. The analysis uses the
statistics of fractional differences in mixing ratio across a range of scales to estimate
the contribution of real variability to differences in noncollocated measurements. The
differences depend on the particular chemical tracer, location and season. We find a range
of behavior: Differences of 50% across horizontal scales 100 km or less are fairly
common for tropospheric water vapor under convective conditions, or carbon monoxide in
regions influenced by biomass burning. Ozone varies by about 4–12% in the lower
stratosphere and 15–25% in the upper/middle troposphere across scales of about 150 km.
The effect of coarse satellite measurement resolution is also estimated by comparing
point measurements to locally averaged measurements and is found to reduce the
occurrence of large tracer differences. The choice of coincidence lengths should be based
on both the scale-dependent variability and a priori estimates of satellite accuracy if
real variability is to remain small relative to satellite measurement uncertainties. For
satellite instrument uncertainties of about 10%, coincidence lengths for ozone should be
less than 50 km in the upper troposphere and less than 100 km in the lower stratosphere.
Citation: Sparling, L. C., J. C. Wei, and L. M. Avallone (2006), Estimating the impact of small-scale variability in satellite
measurement validation, J. Geophys. Res., 111, D20310, doi:10.1029/2005JD006943.
1. Introduction
[2] The detection of climate change and its dependence
on the chemical composition of the atmosphere requires
long-term global monitoring with satellite-borne instruments. Measurements of the chemical composition of the
atmosphere from space are derived from direct radiance
measurements which are converted to chemical concentrations via retrieval algorithms. Satellite observations must be
compared to independent measurements obtained with
accurately calibrated instruments on aircraft, balloon or
ground-based platforms (‘‘correlative measurements’’) soon
after launch and periodically thereafter to ensure that any
instrument drift or bias, which can lead to spurious trends in
the state of the atmosphere, is well understood and can be
corrected for. These ongoing calibration and validation
activities constitute a crucial part of the evaluation of the
global earth system database, and are essential in order to
1
Department of Physics, University of Maryland Baltimore County,
Baltimore, Maryland, USA.
2
QSS Group Inc., Lanham, Maryland, USA.
3
Laboratory for Atmospheric and Space Physics, University of
Colorado at Boulder, Boulder, Colorado, USA.
Copyright 2006 by the American Geophysical Union.
0148-0227/06/2005JD006943$09.00
quantify uncertainties in the climate change signal [see, for
example, King, 1999].
[3] In situ observations of chemical tracers in the UT
(Upper Troposphere) and UT/LS (Upper Troposphere/Lower
Stratosphere) show a high degree of spatial variability at
scales that are well below the resolution of satellite measurements. This small-scale variability is problematic in that
it contributes to differences between satellite measurements
and nearby (but not strictly collocated) in situ or groundbased measurements obtained for the purpose of evaluating
the quality of the satellite measurements. For purposes of
direct comparison, correlative measurements should ideally
sample the atmosphere at the exact times and locations of
the satellite measurement, but this is not always possible
and the number of such direct comparisons is typically
small. Coincidence criteria must be relaxed to some degree,
and this leads to the recurring problem of interpreting the
inevitable differences in observations that are not exactly
collocated. In addition, in situ correlative measurements
are point measurements which must be compared to
lower-resolution satellite observations leading to further
uncertainties and problems of interpretation. The goal of
validation is to understand measurement uncertainties related
to viewing geometry, retrieval algorithms or instrumentation,
but these can be overwhelmed by natural variability when the
tracer field is highly heterogeneous.
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[4] The strong gradients in constituent concentration
fields pose special problems for retrievals from satellite
instruments and other remote sensors, whose resolutions are
low compared to the scale of the atmospheric structures and
whose algorithms typically assume homogeneity along the
line-of-sight. The satellite instruments currently measuring
ozone profiles in the UT/LS (for example, EOS (Earth
Observing System) MLS (Microwave Limb Sounder),
GOME (Global Ozone Monitoring Experiment), SAGE III
(Stratospheric Aerosol and Gas Experiment III), POAM III
(Polar Ozone and Aerosol Measurement)) have horizontal
resolutions ranging from 5 to 960 km and vertical resolutions of about 1 to 5 km [Hoogen et al., 1999; Lucke et al.,
1999; Waters et al., 1999, 2006]. While coarse compared to
observations obtained from aircraft, these are considerably
finer than earlier generations of satellite instruments. As the
horizontal and vertical resolutions of remote sensors have
improved, the ability to account for and/or retrieve information about line-of-sight gradients has also improved
[Worden et al., 2004; Livesey and Read, 2000]. However,
constituent variations along the line-of-sight are still not
adequately understood, nor are the newly developed methods validated against data of appropriate resolution. We
acknowledge that the phrase ‘‘satellite resolution’’ is not
generic; that with the widely different types of remote
sensors in orbit, ‘‘resolution’’ can have many meanings.
Spatial resolution will depend on satellite orbit, as well as
on instrument field of view and even on spectral range. In
addition, most remote sensors have different spatial resolutions in the two horizontal dimensions (e.g., along-track
versus across-track); EOS MLS, for example, samples
approximately 5 km across-track and 160 km along-track
[Waters et al., 2006]. These differences among various
types of satellite measurements make it difficult to say in
general what the impact of small-scale variability will be on
validation, since it will depend on the particular measurement under consideration. Another challenge to defining
‘‘coincidence criteria’’ is that the appropriate coincidence
lengths (see section 3) will also depend on the expected
uncertainty of the satellite measurement. It is important that
natural variability on the scale of the coincidence length is
less than the satellite measurement uncertainties, otherwise
little is gained by the validation exercise. For the EOS
instruments, 10% seems to be a typical value for satellite
precision [Schoeberl, 2004] and is on the order of
the estimated accuracy of several satellite-based trace
gas measurements of ozone profiles such as SAGE III
(5 – 10% [Brogniez et al., 2002]) GOME (10% [Hoogen et
al., 1999]), POAM III (5% [Randall et al., 2003]), and
anticipated from the recently launched EOS Aura instruments MLS [Waters et al., 2006] and OMI. We will
therefore use a nominal value of 10% to illustrate some of
the points we make later.
[5] A number of validation strategies that incorporate
modeling have been developed in an attempt to overcome
the difficulties with noncoincident validation, including data
assimilation [e.g., Lary et al., 2003] and Lagrangian modeling techniques. The latter use trajectories to accumulate
satellite measurements over several days or to propagate
them to new locations and times to increase the number of
coincidences [e.g., Morris et al., 2000; Lu et al., 2000].
Others use Lagrangian air mass sampling to limit compar-
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isons of in situ and satellite measurements to regions where
the air masses have similar origins [Schwab et al., 1996] or
to sample multiple times along the flow as in the Match
technique [Rex et al., 1999]. Other approaches take the
quasi-isentropic nature of stratospheric transport into account by using potential temperature and potential vorticity
(PV) as flow-tracking coordinates, which may increase
coincidences to the extent that it allows comparison of
measurements separated by larger distances but with a
common recent history [Schoeberl and Lait, 1991; Redaelli
et al., 1994; Lary et al., 1995]. However, the advantage of
these methods is not always clear [Morris et al., 2004; Lait
et al., 2004], as they are not applicable at low latitudes, and
the PV/tracer correlation is often too weak to be useful.
While providing some additional assessments of satellite
measurement quality, these different approaches to validation introduce some measure of uncertainty due to the
meteorological analyses or Lagrangian computations themselves and so will likely continue to be used in conjunction
with direct comparisons.
[6] In regions such as the LS polar vortex edge or the UT/LS,
assessing the impact of small-scale variability in tracer fields
is particularly difficult because these are transition zones
between chemically distinct air masses that are being stirred
together by the winds. Stratosphere-troposphere exchange
(STE) dynamical processes such as tropopause folds blend
low water vapor/high ozone stratospheric air with high
water/low ozone tropospheric air resulting in thin vertical
layers and horizontal filaments [Orsolini et al., 1995; Wu et
al., 1997]. Stretching and folding by the winds cascades
large-scale tracer structure to small scales, resulting in
a complex multiscale interleaving of air with different
chemical properties as demonstrated in many numerical
simulations and observed in satellite imagery [for example,
Sutton et al., 1994; Appenzeller et al., 1996]. Certainly the
concept of ‘‘sampling the same air mass’’ becomes muddy in
regions where the boundary between air masses is highly
convoluted over a wide range of scales.
[7] The goal of the work presented here is to provide
some perspectives on statistical properties of small-scale
variability in trace gases on length scales that are relevant
for satellite data validation, and to provide some quantitative estimates of the contribution of natural variability to
differences in correlative measurements under a range of
dynamical conditions. We begin in section 2 with a discussion of data sources and statistical methods, and define
statistical ensembles with respect to region, season and
prevailing meteorology. It is impossible to consider all
chemical species under all possible conditions, so this
analysis emphasizes LS, UT/LS, and UT ozone, with some
additional examples of variability in tropospheric water
vapor and carbon monoxide (CO) under different source
and meteorological conditions. Section 3 presents an overview of the variability in LS ozone across a range of scales
as determined by a statistical analysis of the difference
between pairs of measurements separated by a specified
horizontal and vertical distance. In this section we also
quantify the likelihood of observing differences that are
larger than a given value, investigate the isotropy of the
spatial variability to see whether coincidence criteria that
differ for zonal and latitudinal separations are warranted,
and address the problem of defining suitable coincidence
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criteria. The impact of satellite resolutions is also estimated.
A similar analysis is applied to the DC-8 ozone data in
section 4, with a brief analysis of CO and water vapor for
comparison. In section 5 we show that the statistics of
spatial variability have a degree of universality that seems to
hold (approximately) over a wide range of conditions. We
conclude in section 6 with a summary and discussion.
2. Data and Methods
2.1. Aircraft Data
[8] The emphasis in this study is on small-scale horizontal structure for which the high-resolution (2 km) and highprecision aircraft measurements are well suited. There is
less information about vertical structure per se because the
moving aircraft platform does not sample solely in the
vertical direction over a wide enough range of scales for
the type of scale analysis we wish to do here. Nevertheless,
some aspects of vertical variability must be taken into
account in the horizontal structure analysis as described
below. The aircraft data used in this study were collected
during several NASA-sponsored measurement campaigns
over a period of about 15 years and are summarized in
Table 1, which also includes some general remarks about
sources and dynamical conditions. The LS analysis is
based on ozone measurements taken with the dual-beam
ultraviolet absorption instrument [Proffitt et al., 1989;
Proffitt and McLaughlin, 1993] with a precision of about
0.5% (E. L. Richard, personal communication, 2005) on the
NASA ER-2 aircraft at altitudes in the range 18– 21 km.
Because the objective of the winter ER-2 missions was to
sample inside/outside the polar vortex, the high-latitude flight
paths were overwhelmingly across the polar vortex jet, which
could introduce a sampling bias. The analysis of anisotropy
in a later section suggests that the impact of horizontal
anisotropy, in the sense of N/S (North/South) versus E/W
(East/West), is small on typical coincidence scales.
[9] Results for the LS are presented for four statistical
ensembles that encompass a range of variability in LS
ozone: (1) the tropics (25°S – 25°N); (2) the summer Northern Hemisphere (NH, May –November) and summer Southern Hemisphere (SH, December – May) extratropics; (3) the
winter NH middle/high latitudes, outside the polar vortex
and poleward of 30°; and (4) the interior of the NH/SH
winter polar vortices. We define the interior of the polar
vortex as the high-latitude winter region with potential
vorticity >35 pvu (1 potential vorticity unit = 1.0 106
m2 s1 K kg1), a value typical of the edge of the polar
vortex at ER-2 altitudes.
[10] The tropospheric analysis is based primarily on
DC-8 ozone measurements as described by Gregory et al.
[1987] which have a 1-s precision of 1%. The water vapor
[Vay et al., 1998] and carbon monoxide (CO) [Sachse et al.,
1987] measurements have 1-s precisions of 2% and 1%,
respectively. We use the 10-s averaged data for which the
precision should be even better. The high precision of the
aircraft data is particularly important for this study which is
based on the difference of pairs of measurements.
[11] The analysis of the DC-8 data is restricted to the
vertical region from 8 to 13 km, which has been more
extensively sampled relative to the lower troposphere in this
database. This vertical range corresponds to the middle/
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upper troposphere at lower latitudes and the UT/LS at
middle/high latitudes. Results will be presented for the
individual aircraft campaigns because the overall meteorological conditions and source variability for the tropospheric
data tend to organize themselves according to the goals of
the particular campaign. The emphasis is again on ozone,
but for comparison we also show some results for CO in
regions influenced by biomass burning and continental
pollution. Tropospheric ozone and CO are also of interest
in the application of remote sensing data to issues related to
air quality, long-range transport in the middle/upper troposphere, and mixing and transport of chemical tracers in the
tropopause region. In addition, some statistics are also
presented for water vapor because it represents an upper
bound on the variability of atmospheric trace gases, especially under conditions of strong convection.
[12] We make the standard assumption that the statistics,
if not the exact morphological details, of small-scale spatial
structure based on aircraft measurements collocated to
within 30 min or so are the same as if the measurements
were made instantaneously. This ‘‘frozen turbulence’’ assumption is reasonable if a time span of 30 min is temporally collocated as far as the statistics of two-point
variability is concerned; this is plausible even if the spatial
configuration of the tracer field evolves to some degree on
this timescale.
2.2. Statistical Methods
[13] The statistical analysis is based on the computation
of increments in the tracer mixing ratio across a given
distance. Let c(s,z) be a tracer measurement at horizontal
location s and height z and c(s + r, z + dz) be another
measurement separated from the first by a horizontal
distance r and a vertical distance h = jdzj. Scale-dependent
increments in the tracer field are defined by the absolute
value of the fractional difference (in percent) of the two
measurements
jcðs þ r; z þ hÞ cðs; zÞj
Dr;h ¼ 1
100
=2 ½cðs þ r; z þ hÞ þ cðs; zÞ
ð1Þ
The emphasis in this paper on fractional rather than absolute
differences enables us to synthesize results across a wide
range of conditions and widely varying tracer concentrations. The horizontal separation r, vertical separation h, and
tracer increment Dr,h are computed for each pair. Taking
into account the vertical separation allows us to isolate the
contribution from horizontal structure alone, which is our
main concern here; the aircraft data set does not allow a
statistically robust analysis of vertical profiles for which an
extensive sonde data set is more appropriate. Tracer
differences due to horizontal structure alone will be inferred
from the limit Dr = lim Dr,h, i.e., from the limiting statistical
h!0
behavior of the tracer increments as the vertical separation
becomes very small. The two-point statistics of ‘‘horizontal’’ structure reported in this paper are derived from pairs of
measurements whose vertical separation is small in this
sense. For the cases studied here, we have found that Dr,h is
nearly independent of h for a sampling aspect ratio h:r <
1:500. We further define the mean deviations mr,h = hDr,hi
and mr = hDri (note that these are the means of the absolute
3 of 14
4 of 14
Nov 1992, May 1993
May 1995 to Feb 1996
Apr – Jul and Sep 1997
Nov 1999, Jan – Mar 2000
Dec 2002, Jan – Feb 2003
SPADE
STRAT
POLARIS
SOLVE
SOLVE2
Region/Conditions
SH LS high latitude, polar vortex
NH LS mid/high latitude, polar vortex
NH LS mid/high latitude, polar vortex
SH LS tropics-polar, western Pacific, mixing and
transport, filaments, STE
LS transport/chemistry
NH LS tropics-mid latitude transport, STE
NH mid/high latitude, transport
NH mid/high latitude, polar vortex
NH mid/high latitude, polar vortex
Region/Conditions
NH mid-high latitude, polar vortex, surf zone, STE
NW Pacific, Asian continent outflow
NW Pacific, Asian continent outflow, convection
tropical Pacific, clean marine, biomass burning, LRT
tropical Pacific, clean marine, pollution
midwest USA, continental, convection, subsonic
aircraft emissions
North Atlantic Flight corridor, STE
S. Atlantic, SW Africa, Brazil, S. America outflow,
biomass burning
western Pacific, Asian outflow, pollution
Arctic high latitude, Arctic polar vortex, STE
Arctic high latitude, Arctic polar vortex, surf zone
variability, STE
Reference
Wofsy et al. [1994], http://cloud1.arc.nasa.gov/spade
http://cloud1.arc.nasa.gov/strat/
Newman et al. [1999], http://cloud1.arc.nasa.gov/polaris
Newman et al. [2002], http://cloud1.arc.nasa.gov/solve/
http://cloud1.arc.nasa.gov/solveII/
Tuck et al. [1989], http://cloud1.arc.nasa.gov/aaoe/
Turco et al. [1990], http://cloud1.arc.nasa.gov/aase
Anderson and Toon [1993], http://cloud1.arc.nasa.gov/aase2/
Tuck et al. [1997], http://cloud1.arc.nasa.gov/ashoe_maesa/
Reference
Jacob et al. [2003], http://www.gte.larc.nasa.gov/gte_fld.htm#TRACE
Newman et al. [2002], http://cloud1.arc.nasa.gov/solve/
http://cloud1.arc.nasa.gov/solveII/
http://cloud1.arc.nasa.gov/sonex
Fishman et al. [1996], http://www.gte.larc.nasa.gov/gte_fld.htm#TRACE
Anderson and Toon [1993], http://cloud1.arc.nasa.gov/aase2/
Hoell et al. [1996], http://www.gte.larc.nasa.gov/gte_fld.htm#PEM
Talbot et al. [1997], http://www.gte.larc.nasa.gov/gte_fld.htm#PEM
Hoell et al. [1999], http://www.gte.larc.nasa.gov/pem/pemta_dat.htm
Raper et al. [2001], http://www.gte.larc.nasa.gov/pem/PTB_dat.html
http://cloud1.arc.nasa.gov/success
ER2 altitudes 18 – 21 km; DC8, 8 – 13 km. MT, middle troposphere; UT, upper troposphere; LS, lower stratosphere; STE, stratosphere-troposphere exchange; LRT, long-range transport.
a
Aug – Sep 1987
Dec 1988, Jan – Feb 1989
Oct – Dec 1991, Jan – Mar 1992
Mar – Nov 1994
AAOE
AASE1
AASE2
ASHOE/MAESA
Feb – Apr 2001
Nov 1999, Jan – Mar 2000
Dec 2002, Jan – Feb 2003
TRACE-P
SOLVE
SOLVE2
Time
Oct – Nov 1997
Sep – Oct 1992
SONEX
TRACE-A
ER2 Mission
Time
Oct – Dec 1991, Jan – Mar 1992
Sep – Oct 1991
Feb – Mar 1994
Aug – Oct 1996
Mar – Apr 1999
Apr – May 1996
DC8 Mission
AASE2
PEM-West A
PEM-West B
PEM-Tropics A
PEM-Tropics B
SUCCESS
Table 1. Summary of Aircraft Data Used in This Studya
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SPARLING ET AL.: VARIABILITY AND SATELLITE VALIDATION
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Figure 1. Mean tracer increment mr,h in LS ozone versus
vertical separation h, for fixed horizontal separation r =
100 km. The limit mr,h ! mr isolates the contribution from
horizontal variability. h!0
valueq
offfiffiffiffiffiffiffiffiffiffi
the tracer difference), and the standard deviation
2 ffi
Dr of the signed (i.e., not absolute value) tracer
sr =
difference which has zero mean. For the purposes of data
validation, and partly because of sampling characteristics,
our analysis is restricted to horizontal scales less than
400 km in the LS and 200 km in the UT and UT/LS.
[14] In addition to the two-point statistics, we consider the
satellite measurement resolution in an approximate way by
averaging over a segment of the in situ data and computing
the statistics of the difference between the center of the
averaged measurement and an in situ measurement some
distance away. In the following, we will refer to these local
averages as ‘‘satellite’’ measurements. Each such segment
has a mean location (hxi, hyi), and we define the satellite
‘‘footprint’’ L as the average distance from the mean
location: L = h(x hxi)2 + (y hyi)2i1/2 which is a measure
of the horizontal scale over which the time average takes
place. When the flight paths have long straight-line segments, a time average over an interval Dt for a constant
aircraft speed v corresponds to an average over a horizontal
distance r vDt. This is not true in general, particularly for
the more complicated flight paths in some of the DC-8 data.
By varying the time-averaging window, we generate a range
of values for L, and L-dependent statistics are obtained by
conditioning on L. The mean tracer mixing ratio in the
segment is hciL, and the tracer difference now depends on
L,
DLr;h
cðs þ r; z þ hÞ hcðs; zÞi L ¼ 1
100
=2 cðs þ r; z þ hÞ þ hcðs; zÞiL ð2Þ
[15] The horizontal separation is now defined to be the
distance from the point measurement to the center of the
satellite measurement and we will be concerned only with
the mean mLr = hDLr i for sufficiently small h. Note that for
nonzero L, the limit r ! 0 describes the deviation of a point
measurement from the average in a surrounding neighborhood of scale L, and therefore is a measure of the degree of
local representativeness.
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[16] For certain questions it is necessary to go beyond the
first few moments and consider the entire distribution of
increments. The PDF (Probability Distribution Function)
P(Dr) [see, for example, Sparling and Bacmeister, 2001; Hu
and Pierrehumbert, 2001] is the fraction of increments in a
bin centered on Dr. An important question for satellite data
validation is how often geophysical variability would be
expected to overwhelm instrumental or retrieval uncertainties, whose estimation is the purpose of the validation
exercise. Insight can be gained by considering
the cumulaR1
tive distribution function (CDF) Cr(d) = d P(Dr)dDr. Cr(d)
is the fraction of measurement pairs, separated by a
given value of r, for which Dr is greater than a specified
~ r, defined by
value d. We will also consider the median m
mr) = 1/2, and because P(Dr) is normalized, we also have
Cr(~
Cr(0) = 1. The corresponding CDF of the satellite/in situ
differences will be denoted by CLr (d).
3. Horizontal Variability of LS Ozone
[17] In this section we present an overview of the spatial
variability of ozone in the LS by looking at how the
fractional difference of two measurements depends on their
horizontal and vertical separation. It is important to separate
the contributions from vertical and horizontal structure
because the atmosphere is not isotropic in three dimensions,
to establish horizontal coincidence criteria where possible,
and to interpret differences between satellite instruments
with different horizontal and vertical resolutions.
[18] In order to characterize the statistical properties of
horizontal structure, we must first remove the contribution
from the large-scale vertical gradient or strong vertical
layering. One way to do this is to look at the behavior of
mr,h as a function of vertical separation h for fixed horizontal
separation r. The example in Figure 1 shows that mr,h
decreases with decreasing h and as discussed in section 2,
asymptotes to the limiting value mr as h ! 0. For this
example, r = 100 km and across this scale mr ranges from
4– 5% inside the vortex to 8 – 10% in the NH high latitudes.
Figure 1 also points out that horizontal collocation and
vertical resolution cannot be considered independently. This
is especially true for the tropical curve which indicates that
when r = 100 km, the large vertical gradient in the tropics
overwhelms differences due to horizontal structure if the
vertical separation exceeds about 200 m. In such cases, the
interpretation of differences between satellite and in situ
measurements will depend less on the degree of horizontal
collocation and more on the vertical resolution/weighting
function of the satellite measurement.
[19] Before discussing the dependence of the tracer increments on horizontal scale, it is necessary to consider the
shape of the PDF, as it has some bearing on the way in
which the scale dependence is best characterized. The
stretching and folding of atmospheric tracers leads to a
distribution that is non-Gaussian; an example can be seen in
Figure 2 which shows P(Dr) for the NH winter ensemble for
pairs of measurements with a horizontal separation r =
50 km (thick solid line). Here we have retained the sign
of the tracer difference in order to highlight the nonGaussian shape of the PDF (note that Dr was defined as
an absolute value). The generic long-tailed shape is characteristic of filamentary structure of long-lived tracers in
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Figure 2. PDF of tracer increments across horizontal scale
r = 50 km for NH winter LS ozone (thick solid line). The
median is 3% and is characteristic of the width of the
Gaussian core(thick shaded line). The mean mr is 6%, and
the standard deviation sr is 10%. The thin solid line is a
Gaussian with variance sr2 which can be seen to be a poor
representation of the PDF.
which chemically dissimilar air masses are stirred together
by the large-scale winds. Indicated by vertical lines are mr,
~ r, and sr. The shaded curve is a Gaussian with a standard
m
deviation of 3% which is a reasonable fit to the distribution
near its maximum; in this case the median of the full
distribution is close to the standard deviation of the Gaussian core. Also overplotted (thin solid line) is a Gaussian
with variance s2r , clearly a poor description of P(Dr) in that
it overemphasizes the large increments. We do not necessarily expect the distribution of the fractional difference to
be Gaussian, even if the distribution of the differences
themselves is Gaussian, although this could occur in wellmixed regions where the mean tracer concentration is much
larger than the standard deviation. The point here is just to
show that while the variance of a short-tailed distribution
such as a Gaussian is a reasonable measure of typical
variability, it may not be so when the distribution has long
tails.
[20] It is worth noting that long tails are also observed for
the absolute (not fractional) tracer differences as shown for
example by Sparling and Bacmeister [2001] and theoretically by Hu and Pierrehumbert [2001]. The tails do not
arise here because of a small denominator (e.g., in the case
of two independent Gaussian random variables whose ratio
has a long-tailed Cauchy distribution). This is easy to see
from the definition of Dr as a quantity proportional to the
difference of two positive numbers divided by their sum.
The largest possible value of the fractional difference
defined in equations (1) and (2) is 200%, which occurs in
the limit when the two values are very different.
~ r, mr and sr versus horizontal
[21] Figure 3 compares m
separation r for the different ensembles, and shows that sr is
substantially larger than mr, especially at small scales. For
example, at r = 50 km, mr/sr 0.5, while for a zero-mean
Gaussian random variable the two measures are more
similar, mr/sr 0.8. These distinctions are especially
important for long-tailed distributions, because they can
lead to different conclusions about the degree to which
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geophysical variability contributes to differences in observations. For example, with the exception of NH winter, the
median in Figure 3a suggests that real variability for
coincidence scales up to 300 km would still be less then a
nominal satellite accuracy of 10%, while the standard
deviation in Figure 3c suggests that coincidence lengths
should be well below 100 km if natural variability is to
remain less than 10%. With the exception of NH winter, the
mean deviation suggests that coincidence lengths should be
less than about 200 km. The median may underestimate the
impact of small scales on validation, while the standard
deviation overestimates it and, in addition, may be strongly
affected by undersampling. As a compromise, we will focus
on the mean mr in most of the following analysis.
[22] While a proper choice of coincidence length is
unfortunately dependent on an a priori estimate of the
uncertainty of the satellite measurement, an upper bound
can sometimes be established if the tracer field has a welldefined correlation length. Under conditions of statistical
homogeneity, a correlation length is defined as the scale r
beyond which the autocorrelation hc(s + r)c(s)i vanishes.
Assuming homogeneity, we then have h[c(s + r) c(s)]2i =
2[hc2i hc(s + r)c(s)i] 2hc2i which is independent of r
when r exceeds the correlation length. Two measurements
Figure 3. Comparison of single-parameter measures of
horizontal variability in LS ozone and their dependence
on horizontal scale r. (a) Median, (b) mean mr, (c) sr, and
(d) mean mr as in Figure 3b but on a log scale showing that
mr r1/2 for r 10 km.
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scales the measurement precision is small relative to the real
geophysical variability.
[25] Figure 4 presents a summary of the latitudinal and
seasonal dependence of mr for horizontal scales r = 50 and
r = 200 km. There are some gaps in coverage, for example
the summer SH is not well represented in this database. The
mean increments are large in winter and early spring at high
latitudes, most likely because of the breakup of the polar
vortex. Low values occur throughout the NH in summer and
fall. Overall, mr ranges from 1 – 10% for r = 50 km and 2 –
17% for r = 200 km. Figure 4 (bottom) shows that, for an
estimated satellite uncertainty of 10%, coincidence lengths
up to 200 km may be appropriate in NH summer and fall,
but are too large for validation during NH winter and spring.
Figure 4. Dependence of mean mr on latitude and season
for LS ozone increments across (top) 50 km and (bottom)
200 km.
separated by a distance larger than this are uncorrelated and
cannot reasonably be compared. More generally, an upper
bound for the coincidence length is the scale beyond which
the increment statistics become independent of scale.
Figure 3 suggests that this scale is 300– 400 km, in agreement with Schoeberl et al. [2002], except for the NH winter
ensemble where the mean increment shows no sign of
leveling off as the separation distance increases. This occurs
because the increments become dominated by the large-scale
latitudinal gradient in ozone during this time of year.
[23] Figure 3d shows the same data as in Figure 3b,
except plotted on a log scale to illustrate a scaling regime
described to a good approximation by the power law mr rp
where p 0.5; the precise value of the exponent is of
no concern to us here [see Tuck and Hovde, 1999]. Because
p < 1, the mean increment is more sensitive to horizontal
separation at the smaller scales. In NH winter, the power
law extends to at least several hundred km, with no obvious
upper bound on the coincidence length over this range of
scales. In general, and for the scale-invariant case in
particular, a coincidence length should be chosen so that
the geophysical variability does not dominate the expected
accuracy of the satellite measurement.
[24] At the smallest scales, the tracer increments become
more dependent on instrument precision. For r = 2 km,
Figure 3d shows that mr inside the polar vortex is on the
order of the precision of the ozone measurement. At larger
3.1. Isotropy and Zonal Versus Meridional
Coincidence Criteria
[26] It is common for coincidence criteria to be defined
differently in the zonal and meridional directions. To see if
this is justified it is necessary to investigate whether the
tracer increments depend on the orientation of the separation
between the two measurements. Long-lived LS tracers
often have large-scale meridional gradients, but the issue
here is whether the spatial structure in LS ozone is horizontally anisotropic on the smaller scales relevant for data
validation.
[27] The question of isotropy of the small-scale variability
is best addressed by considering the high-latitude winter
variability where we might expect the largest anisotropy.
Small-scale structure might be anisotropic in the NH winter,
for example, because vortex filaments tend to elongate in
the direction of the principal strain axis and thin in the
transverse direction. For each pair of measurements separated by horizontal distance r, the orientation of the separation vector connecting the two points is also computed. In
order to look at NS/EW (‘‘geographic’’) isotropy, we define
an orientation angle y by siny = reD8/r where re is the earth
radius and D8 is the latitude separation. The angle y is a
measure of the orientation of the separation vector; y = 0°
(90°) if the two points are separated E/W (N/S), and
anisotropy is defined as a dependence of the two-point
statistics on y.
[28] Figure 5 is a plot of the conditional average hDrjyi
versus y for horizontal separation r = 200 km in the winter
mid/high latitudes, conditions under which the anisotropy
would be expected to be large. Shown for comparison are
the results for the remainder of the ER-2 data. In the winter
extratropical SH, where the structure is more nearly zonal,
the mean increment shows a small overall increase as the
orientation changes from E/W to N/S. In the NH on the
other hand, the mean increment is largest when y is between
30– 60°. This is partly due to the fact that many of the NH
winter flights crossed the edge of the polar vortex when it
was distorted or off the pole. Overall, anisotropy effects
appear to be small, at least on the smaller scales relevant for
data validation, and do not support substantially different
coincidence criteria for meridional versus zonal separations.
It is important to note, however, that the ER-2 flight paths
were overwhelmingly N/S oriented, and it is possible that
large contrasts in the E/W direction were not adequately
sampled. We also note that horizontal anisotropy would
perhaps be better defined in terms of the large-scale PV
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when r < L. In this case, the in situ measurement lies within
the satellite footprint and mLr is then a measure of the local
variability within the footprint. For r ! 0, mLr becomes the
difference between a point measurement and a surrounding
neighborhood average and is therefore a measure of the
representativeness of a point measurement, which is on the
order of a few percent. (We note that this average is a 1-D
average over a flight segment; for straight flight segments,
this underestimates a similar 2-D average that weights
measurements according to their distance from the center.)
Figure 5. Isotropy of horizontal structure in LS ozone,
shown by the conditional mean hDrjyi for increments
across horizontal distance r = 200 km in the NH and SH
winter at middle/high latitudes and for all other cases. y is
the orientation angle of the separation; y = 0°(E/W), y =
90°(N/S).
gradient or direction of the large-scale wind instead of a
fixed geographic orientation. Konopka et al. [2004] has
argued from model simulations that along-flow mixing is
substantially greater than across-flow mixing and Hu and
Pierrehumbert [2001] also find evidence for anisotropy in
model simulations.
3.2. Effects of Resolution: Comparing Low-Resolution
Satellite Data to Point Measurements
[29] A satellite measurement is not a point measurement,
but is rather an integration over some extended region of
space, defined in the vertical by the weighting function and
in the horizontal by the satellite footprint. High-resolution
aircraft measurements provide information only along 1-D
transects through the tracer field, but by averaging over
small segments of the flight path we can gain some insight
into the impact of satellite measurement resolution on the
differences between satellite and in situ measurements. In
this section we compute statistics more relevant for the
satellite/in situ comparison by considering a point measurement a distance r away from a segment of data that has been
locally averaged over a length scale L to take into account
the limited horizontal resolution of the satellite measurement, as defined earlier in equation (2). This is clearly an
approximation in that the local geometry of the flight
path may be a poor representation of the actual
averaging volume, which depends on the particular satellite
instrument.
[30] The satellite/in situ mean difference mLr for satellite
footprint L = 200 km is shown in Figure 6 as a function of
horizontal separation r. As expected mLr is generally smaller
than mr (see Figure 3), especially for the NH winter case.
For the polar vortex ensemble, spatial averaging sometimes
includes data from outside the vortex and across the largescale gradient associated with the vortex edge, which causes
mLr to increase for r > 250 km. Otherwise, the main effect of
degraded resolution is a reduction in the sensitivity of
the measurement differences to the horizontal separation
3.3. Cumulative Distribution Functions
[31] The mean deviation mr provides a useful summary of
the spatial variability, but gives no information about how
often geophysical variability might overwhelm instrumental
or retrieval uncertainties. We can gain quantitative insight
into this important problem from the CDFCr(d), the fraction
of tracer increments at scale r that exceed d (%). Cr(d) is
shown in Figure 7 for separations r = 50 and 200 km, and
CLr (d) is overplotted for the same cases with a satellite
footprint L = 200 km (thin lines). As expected, the averaging reduces the occurrence of large differences, especially
for r = 50 km, but the overall effect of resolution on the
cumulative distribution is rather small. This is the effect of
intermittency; a small number of extreme values can have a
large effect on the moments, but little effect on the cumulative distribution except in the tails. The median values,
where the CDF = 0.5, are fairly insensitive to averaging and
are rather small (2 – 5%) in all cases for r = 50 km,
increasing to 4 – 8% for r = 200 km. The cumulative
distributions in Figure 7 demonstrate that about 40% of
the measurement pairs separated by 200 km have differences larger than 10% in the NH winter middle/high
latitudes. Instrumental or retrieval uncertainties that are
about 10% would then be masked by geophysical variability
in about 40% of the comparisons, unless the coincidence
length is well below 200 km. When the separation distance
is reduced to r = 50 km, only 15% of the measurement pairs
have differences exceeding 10%. Figure 7 also indicates that
for a coincidence length of 50 km, it is highly improbable
Figure 6. Mean difference mrL between a simulated
satellite measurement of LS ozone with footprint L =
200 km and a point measurement as a function of their
horizontal separation r.
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ultimately comes from the large-scale gradients across air
masses when they are stirred together. The fractional difference between the most probable tracer values in the
altitude range 4 – 6 km and those from 10 to 12 km is about
100% for CO, 150% for ozone and 200% for water vapor
(the maximum possible value): this 1:1.5:2 scaling is
reflected in the overall scaling of the curves in Figure 8b.
[34] In addition, a feature not seen in the corresponding
LS plots is the structure at h < 200 m, which is also evident
in data from the individual missions. Analysis of simulated
data with randomly placed Gaussian structures showed
that very thin layers with strong contrasts across about
100– 200 m produced similar results and could be the origin
of this structure; this is also supported by the scale analysis
of thin vertical layers during PEM-West A [Newell et al.,
1996]. There is an intermediate plateau in which mr,h is
insensitive to vertical separation, while at larger scales of
about 600– 700 m, the large-scale vertical gradient of the
background atmosphere becomes apparent. Small-scale vertical structure is also seen in the lower-latitude middle/upper
troposphere data (Figure 8a), especially for water vapor.
The large-scale vertical gradient in water vapor becomes
apparent for h > 700 m, but there is little dependence on
vertical separation for CO and ozone. At smaller horizontal
scales (r = 50 km, not shown) the results are similar, except
that mr,h is smaller by about a factor of 2.
Figure 7. Comparison of the cumulative distribution
(CDF) of LS ozone increments between two points and
between a point and a simulated satellite measurement with
footprint L = 200 km. The CDF is the fraction of differences
that exceed d%. (top) r = 50 km and (bottom) r = 200 km.
that tracer differences greater than about 25% could be
attributed to real spatial variability.
4. Horizontal Variability of Ozone, CO, and
Water Vapor in the Middle and Upper Troposphere
[32] We now turn to an analysis of the DC-8 data in order
to characterize horizontal variability in the middle and upper
troposphere. As before for the LS ozone analysis, we first
consider tracer increments across a fixed horizontal scale,
and look at the dependence of mr,h on vertical separation in
the limit h ! 0 to isolate contributions from horizontal and
vertical structure. Again, the flight paths have less information about vertical profiles, as there are far fewer pairs of
measurements for which r is very small and h is large.
[33] A plot of mr,h versus vertical separation h at fixed
horizontal scale r = 150 km is shown in Figure 8b for the
middle-/high-latitude UT/LS measurements of ozone, CO
and water vapor. The plots for the different chemical species
are similar in shape, differing mainly in the overall magnitude of the tracer increments, which are smallest for CO and
largest for water vapor. This reflects the common origin of
the tracer variability in the middle-/high-latitude UT/LS,
which includes stratosphere-troposphere exchange (STE)
processes acting on the large-scale differences in the mixing
ratios characteristic of stratospheric and tropospheric air
masses. The magnitude of the contrast across small scales
Figure 8. Mean tracer increment mr,h in UT and UTLS
water vapor, ozone and carbon monoxide versus vertical
separation h, for fixed horizontal separation r = 150 km.
(a) Low-/middle-latitude UT and (b) middle-/high-latitude
UTLS.
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Figure 9. Mean tracer increment mr versus horizontal
separation r for UT and UTLS ozone based on data from
various DC-8 missions. The inset is the same, but plotted on
log axes, and shown also for comparison is y = r1/2.
[35] The asymptotic behavior in the limit h ! 0 is not as
clear in the UT as in the LS, thus our ability to separate the
contributions from vertical structure is more uncertain for
the tropospheric data. To minimize the impact of vertical
structure, the following analysis of horizontal variability is
based only on measurements that have a vertical separation
of less than 50 m. We recognize that the values reported for
horizontal variability in the UT/LS could be overestimates
by a few percent due to contributions from very thin vertical
layers. This is unavoidable, because a cutoff value of h that
is too small leaves too few measurements for a proper
analysis.
[36] Figure 9 shows the dependence of mr on horizontal
scale for UT/LS ozone for all DC-8 missions. Curves
typically level off after about 150 km, indicating that the
small-scale structure has a horizontal correlation length of
about 150 km under a wide range of conditions. Strictly
speaking, a correlation length is a separation scale beyond
which tracer increments become independent of scale. The
plots indicate in some cases a peak instead. This could be
the first peak in a damped oscillation indicative of quasiperiodic structure with characteristic scale of about 150 km,
which shows up in studies of simulated 1-D datastreams.
The decrease in mr beyond the peak could also be due in part
to insufficient data for large values of r, so that large, but
infrequent, tracer gradients are undersampled. For ozone,
mean increments across scale r = 150 km are in the range
13– 25% and increments of 10% occur across scales in the
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range 15– 70 km. The results for CO and water vapor (not
shown) are similar, except that the increments for CO are
about half those of ozone, and for water vapor they are more
than twice as large. These results suggest that the horizontal
coincidence length for validation should be less than 150 km
in the middle and upper troposphere, if the satellite measurement uncertainty is greater than 25%. If the satellite
uncertainty is on the order of 10%, however, coincidence
lengths should be less than 50 km if geophysical variability
is to remain small relative to satellite measurement uncertainties. The inset in Figure 9 is a log-log plot of the same
data, with the line y = r1/2 overplotted for reference. This
shows that, as in the LS, mr varies approximately as r1/2.
[37] There is substantial variation in the statistics among
the individual flights for each mission. The mean and
median increments in ozone across horizontal separation
scales r = 40 and 120 km are plotted in Figure 10, where
each symbol represents a single flight. There is some
overlap in that increments across scales of 40 km on some
days are comparable to those across 120 km on other days.
By definition, half of the measurement differences are larger
than the median, and as shown later, about 1/3 are larger
than the mean. Mean increments larger than 10% are found
often and over a wide range of conditions even for small
(40 km) separations. Taking an optimistic view, the median
plot shows that for the majority of the individual flights,
half of the measurement pairs differ by less than 10% if the
horizontal separation is 40 km. Overall, Figure 10 argues
that a coincidence distance of about 100 km would be too
Figure 10. (top) Mean mr and (bottom) median tracer
increments across horizontal scales r = 40 and 120 km. Each
plotted symbol corresponds to an individual flight.
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Figure 11. Cumulative distributions of (left) Dr and
(right) DrL for horizontal separation r = 120 km and
satellite footprint L = 120 km. (top) Ozone, (middle) carbon
monoxide and (bottom) water vapor.
large to validate tropospheric ozone under most conditions
if the satellite measurement accuracy is 10– 25%; in this
case, the coincidence distance should be less than 40 km.
[38] The distribution P(Dr) (not shown) for the DC-8 data
has the generic long-tailed shape, similar to that seen for the
LS ozone data. The cumulative two-point distributions Cr(d)
for ozone (Figure 11, top), CO (Figure 11, middle) and
water vapor (Figure 11, bottom) are shown in Figure 11
(left) for a measurement separation r = 120 km for several
representative missions that span the range of variability.
For ozone, the plots show that the fraction of measurement
pairs whose fractional difference exceeds 10% ranges from
about 0.4 in the UT during Trace-A (TRA) to 0.6 during
PEM Tropics-A (PTA), with intermediate values of about
0.5 in the winter high-latitude UT/LS. For CO, the largest
differences were found for the TRACE-P (TRP) mission,
which sampled highly polluted air that was close to the
source, off the east coast of China [Jacob et al., 2003]. The
smallest increments were observed during PEM-Tropics B
(PTB) for which CO levels were high, but sampled further
away from the biomass burning sources in South America.
In this case, small fractional differences could arise from
large mean values in the denominator of equation (1) but
weaker small-scale gradients (e.g., greater homogeneity)
due to a longer exposure to small-scale mixing. It is not
surprising that the plots for UT water vapor indicate a high
degree of variability; 0.9 of the measurement pairs in the UT
were different by more than 10% under conditions of strong
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convection during PEM-Tropics B. In the high-latitude UT/
LS (SOLVE), about 0.45 differed by more than 10%.
[39] To estimate the effect of the coarse spatial resolution
of a satellite measurement, we again compute the CDFs of
fractional differences between a spatially averaged segment
of data and a point measurement. The cumulative distributions CLr (d) for ozone, CO and water vapor for a separation
r = 120 km and satellite footprint L = 120 km are shown for
the same cases in Figure 11 (right). We expect spatial
averaging to reduce the fractional differences, and examination of the corresponding left and right plots shows this to
be the case. This is particularly true for the TRACE-P ozone
and CO data, which show strong small-scale structure due
to the proximity to sources.
[40] The effect of the averaging is most pronounced in the
tails of the distributions, reducing the frequency of large
fractional differences. The large reduction in the tails of the
CDF for the SUCCESS water vapor data is due in part to the
‘‘near field’’ sampling of aircraft emissions [Toon and
Miake-Lye, 1998] with strong small-scale inhomogeneities.
The effect of resolution is smaller, however, on the differences that are more typically observed and hence more
relevant for satellite data validation. With spatial averaging,
median two-point increments of 8 – 14% are reduced to 5 –
13% for ozone, from 6 – 11% to 3– 7% for CO and from
10– 50% to 8 – 30% for water vapor. We have also found
that there is little difference between Cr(d) and CLr (d) when
the satellite footprint is reduced to 50 km (not shown). It
should be emphasized again, however, that simple averaging over a flight path segment could be a poor approximation to averaging over the actual satellite measurement
volume.
5. CDFs of Scaled Increments
[41] The CDFs Cr(d) quantify the likelihood of observing
increments larger than an amount d over a horizontal scale r,
an important quantity in assessing the impact of natural
variability, and also a means to estimate the amount of
correlative data required for adequate validation. The variability in the CDFs Cr(d) in LS ozone (Figure 7) and middle
and upper tropospheric ozone, CO, and water vapor
(Figure 11) is not surprising considering the fact that this
data set samples a range of sources and meteorological
conditions from the middle troposphere to the lower stratosphere. Despite this variability, the CDFs of tracer increments normalized by the mean mr appear to have a similar
form, allowing for a simpler synthesis of the statistical
properties of trace gases. We define the CDF of the scaled
increments by Cr(d) = fraction of measurements for which
Dr/mr d. The normalization takes into account the
different source strengths, for example, the large-scale
gradients in tracers across the tropopause or the intensity
of convective, biomass burning or pollution sources.
[42] Figure 12 overplots Cr(d) for the individual LS ozone
ensembles as in Figure 7, together with the CO and water
vapor curves in Figure 11 (left). Curves are shown for r =
120 km, but the behavior for other values of r in the range
30– 150 km is similar. The rescaling does not remove all of
the differences in the individual curves, especially for water
vapor; this is most likely due to the shorter atmospheric
residence time of water vapor relative to that of ozone and
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Figure 12. Cumulative distributions of normalized twopoint increments for LS ozone and UTLS/UT ozone, CO
and water vapor at scale r = 120 km. The two-point
increment CDFs in Figure 11 (left) are replotted here in
terms of normalized increments d = Dr/mr, and the CDFs for
LS ozone are as in Figure 7, except for r = 120 km. The
water vapor CDFs are shown with a dashed line.
CO. There are also substantial differences in the tails that
are not apparent on the scale of the graph and are partly due
to undersampling. In any case, our main concern, from the
point of view of data validation, is the typical variability.
The similarity of the curves allows us to say, for example,
that about one third of the increments will exceed the mean
mr over a wide range of conditions, in different parts of the
atmosphere, for different chemical tracers and across different scales.
[43] The shape of the CDF is broadly consistent with the
stretched exponential form exp(ad p) with 0.6 < p < 1,
where the value of the exponent p depends on scale and to
some extent on atmospheric conditions. A similar form, but
for the increment PDFs, is suggested by theoretical work on
passive scalar mixing [Hu and Pierrehumbert, 2001], and as
found from LS ozone data [Sparling and Bacmeister, 2001].
The similarity of the CDFs for the scaled increments also
argues for some measure of universality as suggested by
Shraiman and Siggia [2000] for passive scalar ‘‘turbulence.’’ This raises some interesting questions that are
outside the scope of the current work; a more in-depth
investigation is underway and will be reported in a future
paper.
6. Summary and Discussion
[44] The main goal of this paper was to provide some
perspectives on naturally occurring variability in chemical
constituent fields in the context of noncoincident satellite
measurement validation. Analysis of increments in tracer
mixing ratio across a range of scales shows non-Gaussian
behavior due in part to the multiplicative process of stretching and folding. It is important to take this into account to
properly assess the impact of small scales and formulate
coincidence criteria, and we have argued that for longtailed distributions the mean and median increments
are more representative of the typical variability, relative
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to the standard deviation, especially when the tail is not
adequately sampled.
[45] The analysis presented here can be used to set some
realistic bounds on coincidence length based on the way the
differences between two measurements depend on scale. A
correlation length, when it exists, can be used to define an
upper bound for the coincidence length. For LS ozone, the
correlation length is 350– 400 km, except in the NH winter
surf zone (mid latitude regions stirred by Rossby waves),
where the lack of a correlation length indicates scale
invariance over the range of scales considered (0 –
400 km). In the middle and upper troposphere the scaling
range is smaller and we find a correlation length on the
order of 100– 150 km under a wide range of conditions. For
distances less than the correlation length, mr scales approximately as r1/2 in both the stratosphere and troposphere.
Across horizontal scales of 150 km, mr ranges from 4 to
12% for LS ozone and 15 to 25% for MT/UT ozone. The
variability can be substantial even at smaller scales; mean
ozone increments of 9 – 16% occur across scales of 50 km in
the middle and upper troposphere, and 2 – 7% in the LS.
Increments larger than 30% across 100 km routinely occur
for the shorter-lived water vapor, with median increments as
high as 50% in some cases.
[46] The impact of small-scale variability on satellite data
validation depends on the degree of heterogeneity in the
observed field relative to the instrumental or retrieval
measurement errors. The choice of optimal conditions for
validation, for example coincidence criteria, requires some
prior estimate of the accuracy and precision of the satellite
measurement. The coincidence length should be smaller
than the scale at which geophysical variability begins to
dominate the estimated satellite measurement uncertainty,
and a reasonable choice for the coincidence length rc is the
scale at which mrc is below the a priori estimate of satellite
uncertainty. Our results show that for tropospheric ozone,
validation of satellite measurements by direct comparison
with noncoincident measurements is likely to be a problem
when the measurements are separated by more than 50 km
and the estimated satellite uncertainties are on the order of
10% or less. For similar satellite uncertainties, the coincidence length should be less than 200 km for LS ozone
except in the NH mid/high latitudes where it should be less
than 100 km. We note that in situ measurement uncertainties
will also contribute to measurement differences; however
they should be much smaller than those associated with
satellite measurements if they are to be useful for validation
purposes. Our results suggest that the suggested 6 hr/100 km
coincidence criteria for validation of tropospheric species,
and the half-day/200 km(lat)/1000 km(lon) criteria for
stratospheric species [Froidevaux and Douglass, 2001]
may not be sufficient to insure that real geophysical
variability does not dominate measurement uncertainties.
In addition, vastly different coincidence lengths in the zonal
and meridional directions do not seem warranted, but the
possibility remains that along-jet and across-jet variability
could be different and may have to be taken into account.
[47] In order to estimate the effect of coarse satellite
resolution, the two-point analysis was modified by comparing the difference between a neighborhood average around
one point to a second point some distance away. As
expected, the occurrence of large tracer differences was
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reduced somewhat for a satellite footprint of 200 km(LS)
and 120 km(UTLS/UT) relative to the two-point case.
Using the two-point statistics to estimate the difference
between a lower-resolution satellite measurement and a
point measurement can therefore sometimes overestimate
the contribution of real variability and in general should be
regarded as an upper bound. Additional studies (not shown)
indicate that the statistics of satellite/in situ differences are
very similar to the two-point statistics when the satellite
footprint is 50 km or smaller. Our attempt to take into
account the satellite resolution in this way is constrained by
the 1-D sampling characteristics of the aircraft platform.
The average was based on temporally nearby measurements, but the spatial distribution of those measurements
depends on the geometry of the flight path segment and may
be a poor approximation to the actual volume sampled by
the satellite measurement. Given these uncertainties, the
two-point differences provide a less ambiguous, if somewhat overestimated, assessment of the contribution of real
variability to measurement comparisons. A better approximation would require averaging the two-point increments
over the actual satellite footprint, which would, in turn,
require sampling designed for that purpose. It may also be
possible to use the two-point PDF to appropriately average
over the actual satellite footprint. Our results suggest that
the two-point differences are a reasonable approximation for
the typical variability if the satellite footprint is smaller than
about 100 km. Validation of satellite measurements with a
broad vertical weighting function remains problematic especially in situations where strong vertical layering below
the satellite resolution occurs. The focus in this paper was
on horizontal variability, but the methods could be applied
to analysis of vertical structure using, for example, airborne
or ground-based lidar data.
[48] There were a few statistical features that were found
to be common to the various data sets considered here, and
that could perhaps lead to some new ways to think about
noncoincident satellite data validation. The mean tracer
increments show an approximate r1/2 dependence for separation distances less than the correlation length, and the
likelihood that a measurement will exceed the mean mr is
about 1/3, a fact that follows from the nearly universal form
of the CDF of the normalized differences d = Dr/mr. These
results hold for a wide range of conditions, and for different
tracers in the middle and upper troposphere as well as LS
ozone, suggesting that they follow from the properties of the
underlying dynamics for the longer-lived species. In an
aircraft validation campaign, one can compute the tracer
increments from the aircraft data to characterize the local
conditions. The CDFs could then provide some perspective
on the likelihood that the observed differences have a strong
geophysical component. Another way in which these methods might be utilized in a validation campaign would be to
compute differences between satellite and correlative measurements as a function of separation and to look at their
asymptotic properties in the limit as r ! 0. In the limit of
perfect measurements, where the geophysical variability
dominates, one should find these differences approaching
zero as r ! 0, with a behavior proportional to r1/2 if the two
measurements are coincident to within 30 min or so. The
differences will asymptote to some nonzero value in this
limit if there is a bias, and the asymptotic value represents
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the uncertainty in the measurement, assuming that the
instrumental error for the in situ measurement is well below
that of the satellite measurement. This method removes the
requirement of exact spatial coincidence, utilizing instead
the asymptotic properties of the differences in the limit of
strict collocation. Of course another way to detect bias is to
compare the peak (most probable) value of the satellite and
correlative one-point PDFs. While this requires a large
number of both satellite and in situ measurements at about
the same place and time, strict collocation is not necessary.
Finally, when evaluating the quality of the satellite measurement under conditions of strong variability, the nonGaussian signature of the two-point statistics of real tracer
variability may be of some use in deciding whether observed differences look geophysical, especially if the differences due to instrumentation or retrieval are Gaussiandistributed.
[49] Acknowledgment. The authors would like to acknowledge the
EOS Interdisciplinary program and the NASA/ACMAP program for
support of this work.
References
Anderson, J. G., and O. B. Toon (1993), Airborne Arctic Stratospheric
Expedition II: An overview, Geophys. Res. Lett., 20, 2499 – 2502.
Appenzeller, C., H. C. Davies, and W. A. Norton (1996), Fragmentation of
stratospheric intrusions, J. Geophys. Res., 101, 15,071 – 15,078.
Brogniez, C., A. Bazureau, J. Lenoble, and W. P. Chu (2002), Stratospheric
Aerosol and Gas Experiment (SAGE) III measurements: A study on the
retrieval of ozone, nitrogen dioxide, and aerosol extinction coefficients,
J. Geophys. Res., 107(D24), 4758, doi:10.1029/2001JD001576.
Fishman, J., J. M. Hoell, R. D. Bendura, R. J. McNeal, and V. W. J. H.
Kirchhoff (1996), NASA GTE TRACE A Experiment (September –
October 1992): Overview, J. Geophys. Res., 101, 23,865 – 23,879.
Froidevaux, L., and A. Douglass (Eds.) (2001), Earth Observing
System (EOS) Aura Science Data Validation Plan, NASA,
Washington, D. C. (Available at http://aura.gsfc.nasa.gov/images/
project/aura_validation_v1.0.pdf).
Gregory, G. L., C. H. Hudgins, J. Ritter, and M. Lawrence (1987), In situ
ozone instrumentation for 10-Hz measurements: Development and
evaluation, paper presented at Sixth Symposium on Meteorological
Observations and Instrumentation, Am. Meteorol. Soc., New Orleans,
La., 12 – 16 Jan.
Hoell, J. M., D. D. Davis, S. C. Liu, R. Newell, M. Shipham, H. Akimoto,
R. J. McNeal, R. J. Bendura, and J. W. Drewry (1996), Pacific
Exploratory Mission-West A (PEM-West A): September – October
1991, J. Geophys. Res., 101(D1), 1641 – 1654.
Hoell, J. M., D. D. Davis, D. J. Jacob, M. O. Rodgers, R. E. Newell, H. E.
Fuelberg, R. J. McNeal, J. L. Raper, and R. J. Bendura (1999), Pacific
Exploratory Mission in the tropical Pacific: PEM-Tropics A, August –
September 1996, J. Geophys. Res., 104(D5), 5567 – 5584.
Hoogen, R., V. V. Rozanov, and J. P. Burrows (1999), Ozone profiles from
GOME satellite: Algorithm description and first validation, J. Geophys.
Res., 104, 8263 – 8280.
Hu, Y., and R. T. Pierrehumbert (2001), The advection-diffusion problem
for stratospheric flow: Part II. Probability distribution function of tracer
gradients, J. Atmos. Sci., 59, 2830 – 2845.
Jacob, D. J., J. H. Crawford, M. M. Kleb, V. S. Connors, R. J. Bendura, J. L.
Raper, G. W. Sachse, J. C. Gille, L. Emmons, and C. L. Heald (2003),
Transport and Chemical Evolution over the Pacific (TRACE-P) aircraft
mission: Design, execution, and first results, J. Geophys. Res., 108(D20),
9000, doi:10.1029/2002JD003276.
King, M. D. (Ed.) (1999), EOS Science Plan: The State of Science in the
EOS Program, 397 pp., NASA, Washington, D. C.
Konopka, P., R. Spang, G. Gunther, R. Muller, D. S. McKenna,
D. Offermann, and M. Riese (2004), How homogeneous and isotropic is
stratospheric mixing?: Comparison of CRISTA-1 observations with
transport studies based on the Chemical Lagrangian Model of the Stratosphere (CLaMS), Q. J. R. Meteorol. Soc., 128, 1 – 13.
Lait, L. R., et al. (2004), Non-coincident inter-instrument comparisons of
ozone measurements using quasi-conservative coordinates, Atmos. Chem.
Phys., 4, 2345 – 2352.
Lary, D. J., M. P. Chipperfield, J. A. Pyle, W. A. Norton, and L. P.
Riishojgaard (1995), Three dimensional tracer initialisation and general
13 of 14
D20310
SPARLING ET AL.: VARIABILITY AND SATELLITE VALIDATION
diagnostics using equivalent PV latitude-potential temperature coordinates, Q. J. R. Meteorol. Soc., 121, 187 – 210.
Lary, D. J., B. Khattatov, and H. Y. Mussa (2003), Chemical data assimilation: A case study of solar occultation data from the ATLAS 1 mission
of the atmospheric trace molecule spectroscopy experiment (ATMOS),
J. Geophys. Res., 108(D15), 4456, doi:10.1029/2003JD003500.
Livesey, N. J., and W. G. Read (2000), Direct retrieval of line-of-sight
atmospheric structure from limb sounding observations, Geophys. Res.
Lett., 27(6), 891 – 894.
Lu, C. H., G. K. Yue, G. L. Manney, H. Jager, and V. A. Mohnen (2000),
Lagrangian approach for Stratospheric Aerosol and Gas Experiment
(SAGE) II profile intercomparisons, J. Geophys. Res., 105, 4563 – 4572.
Lucke, R. L., et al. (1999), The Polar Ozone and Aerosol Measurement
(POAM) III instrument and early validation results, J. Geophys. Res.,
104(D15), 18,785 – 18,800.
Morris, G. A., J. F. Gleason, J. Ziemke, and M. R. Schoeberl (2000),
Trajectory mapping: A tool for validation of trace gas observations,
J. Geophys. Res., 105, 17,875 – 17,894.
Morris, G. A., B. Bojkov, L. R. Lait, and M. R. Schoeberl (2004), A review
of the Match technique as applied to AASE-2/EASOE and SOLVE/
THESEO, Atmos. Chem. Phys. Disc., 4, 1 – 53.
Newell, R. E., Z.-X. Wu, Y. Zhu, W. Hu, E. V. Browell, G. L. Gregory,
G. W. Sachse, J. E. Collins Jr., K. K. Kelley, and S.-C. Liu (1996),
Vertical fine-scale atmospheric structure measured from NASA DC-8
during PEM-West A, J. Geophys. Res., 101, 1943 – 1960.
Newman, P. A., D. W. Fahey, W. H. Brune, M. J. Kurylo, and S. R. Kawa
(1999), Preface to POLARIS special section, J. Geophys. Res., 104,
26,481 – 26,495.
Newman, P. A., et al. (2002), An overview of the SOLVE/THESEO 2000
campaign, J. Geophys. Res., 107(D20), 8259, doi:10.1029/
2001JD001303.
Orsolini, Y. J., P. Simon, and D. Cariolle (1995), Filamentation and layering
of an idealized tracer by observed winds in the lower stratosphere, Geophys. Res. Lett., 22, 839 – 842.
Proffitt, M. H., and R. L. McLaughlin (1993), Fast-response dual-beam
UV-absorption ozone photometer suitable for use on stratospheric
balloons, Rev. Sci. Instrum., 54, 1719 – 1728.
Proffitt, M. H., et al. (1989), In situ ozone measurements within the 1987
ozone hole from a high-altitude ER-2 aircraft, J. Geophys. Res., 94,
16,547 – 16,556.
Randall, C. E., et al. (2003), Validation of POAM III ozone: Comparisons
with ozonesonde and satellite data, J. Geophys. Res., 108(D12), 4367,
doi:10.1029/2002JD002944.
Raper, J. L., M. M. Kleb, D. J. Jacob, D. D. Davis, R. E. Newell, H. E.
Fuelberg, R. J. Bendura, J. M. Hoell, and R. J. McNeal (2001), Pacific
Exploratory Mission in the Tropical Pacific: PEM-Tropics B, March –
April 1999, J. Geophys. Res., 106(D23), 32,401 – 32,426.
Redaelli, G., et al. (1994), UARS MLS O3 soundings compared with lidar
measurements using the conservative coordinates reconstruction technique, Geophys. Res. Lett., 21, 1535 – 1538.
Rex, M., et al. (1999), Chemical ozone loss in the Arctic winter 1994/95 as
determined by the Match technique, J. Atmos. Chem., 32, 35 – 59.
Sachse, G. W., G. F. Hill, L. O. Wade, and M. G. Perry (1987), Fastresponse, high-precision carbon monoxide sensor using a tunable diode
laser absorption technique, J. Geophys. Res., 92, 2071 – 2081.
Schoeberl, M. R. (2004), Earth observing system missions benefit atmospheric research, Eos Trans. AGU, 85, 177.
Schoeberl, M. R., and L. R. Lait (1991), Conservative coordinate transformations for atmospheric measurements, in The Use of EOS for Studies in
Atmospheric Physics, edited by J. C. Gille and G. Visconti, Proc. Int. Sch.
Phys. Enrico Fermi, CXV, 419 – 430.
D20310
Schoeberl, M. R., et al. (2002), An assessment of the ozone loss during the
1999 – 2000 SOLVE/THESEO 2000 arctic campaign, J. Geophys. Res.,
107(D20), 8261, doi:10.1029/2001JD000412.
Schwab, J. J., R.-J. Pau, and J. Zhang (1996), What constitutes a valid
intercomparison of satellite and in situ stratospheric H2O measurements?,
J. Geophys. Res., 101, 1517 – 1528.
Shraiman, B., and E. D. Siggia (2000), Scalar turbulence, Nature, 405,
639 – 646.
Sparling, L. C., and J. T. Bacmeister (2001), Scale-dependence of tracer
microstructure: PDFs, intermittency and the dissipation scale, Geophys.
Res. Lett., 28, 2823 – 2826.
Sutton, R. T., H. Maclean, R. Swinbank, A. O’Neill, and F. W. Taylor
(1994), High-resolution stratospheric tracer fields estimated from satellite
observations using Lagrangian trajectory calculations, J. Atmos. Sci., 51,
2995 – 3005.
Talbot, R. W., et al. (1997), Chemical characteristics of continental outflow
from Asia to the troposphere over the western Pacific Ocean during
February – March 1994: Results from PEM-West B, J. Geophys. Res.,
102(D23), 28,255 – 28,274.
Toon, O. B., and R. C. Miake-Lye (1998), Subsonic aircraft: Contrail and
cloud effects special study (SUCCESS), Geophys. Res. Lett., 25(8),
1109 – 1112.
Tuck, A. F., and S. Hovde (1999), Fractal behavior of ozone, wind and
temperature in the lower stratosphere, Geophys. Res. Lett., 26, 1271 –
1274.
Tuck, A. F., R. T. Watson, E. P. Condon, J. J. Margitan, and O. B. Toon
(1989), The planning and execution of ER-2 and DC-8 aircraft flights
over Antarctica, August and September 1987, J. Geophys. Res., 94,
11,181 – 11,222.
Tuck, A. F., W. H. Brune, and R. S. Hipskind (1997), Airborne Southern
Hemisphere Ozone Experiment/Measurements for Assessing the Effects
of Stratospheric Aircraft (ASHOE/MAESA): A road map, J. Geophys.
Res., 102, 3901 – 3904.
Turco, R., A. Plumb, and E. Condon (1990), The Airborne Arctic Stratospheric Expedition: Prologue, Geophys. Res. Lett., 17, 313 – 316.
Vay, S. A., B. E. Anderson, G. W. Sachse, J. E. Collins, J. R. Podolske,
C. H. Twohy, B. Gandrud, K. R. Chan, S. L. Baughcum, and H. A. Wallio
(1998), DC-8-based observations of aircraft CO, CH4, N2O, and H2O(g)
emission indices during SUCCESS, Geophys. Res. Lett., 25, 1717 – 1720.
Waters, J. W., et al. (1999), The UARS and EOS Microwave Limb Sounder
Experiments, J. Atmos. Sci., 56, 194 – 218.
Waters, J. W., et al. (2006), The Earth Observing System Microwave Limb
Sounder (EOS MLS) on the Aura satellite, IEEE Trans. Geosci. Remote
Sens., 44(5), 1075 – 1092.
Wofsy, S. C., R. C. Cohen, and A. L. Schmeltekopf (1994), Overview: The
Stratospheric Photochemistry, Aerosols, and Dynamics Experiment
(SPADE) and Airborne Arctic Stratospheric Expedition II (AASE-II),
Geophys. Res. Lett., 21, 2535 – 2538.
Worden, J. R., K. W. Bowman, and D. B. Jones (2004), Two-dimensional
characterization of atmospheric profile retrievals from limb sounding
observations, J. Quant. Spectrosc. Radiat. Transfer, 86, 45 – 71.
Wu, Z., R. E. Newell, Y. Zhu, B. E. Anderson, E. V. Browell, G. L.
Gregory, G. W. Sachse, and J. E. Collins Jr. (1997), Atmospheric layers
measured from the NASA DC-8 during PEM-West B and comparison
with PEM-West A, J. Geophys. Res., 102(D23), 28,353 – 28,366.
L. M. Avallone, Laboratory for Atmospheric and Space Physics,
University of Colorado at Boulder, Boulder, CO 80309, USA.
L. C. Sparling, Department of Physics, University of Maryland Baltimore
County, Baltimore, MD 21250, USA. (sparling@umbc.edu)
J. C. Wei, QSS Group Inc., Lanham, MD 20706, USA.
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