ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-16-1065-2016The importance of temporal collocation for the evaluation of aerosol models with observationsSchutgensN. A. J.schutgens@physics.ox.ac.ukhttps://orcid.org/0000-0001-9805-6384PartridgeD. G.StierP.Department of Physics, University of Oxford, Parks road, Oxford OX1 3PU, EnglandDepartment of Environmental Science and Analytical Chemistry, Stockholm University, Stockholm, SwedenBert Bolin Centre for Climate Research, Stockholm University, Stockholm, SwedenN. A. J. Schutgens (schutgens@physics.ox.ac.uk)29January2016162106510794August201525September20158January201612January2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/16/1065/2016/acp-16-1065-2016.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/16/1065/2016/acp-16-1065-2016.pdf
It is often implicitly assumed that over suitably long periods the mean of
observations and models should be comparable, even if they have different
temporal sampling. We assess the errors incurred due to ignoring temporal
sampling and show that they are of similar magnitude as (but smaller than) actual
model errors (20–60 %).
Using temporal sampling from remote-sensing data sets, the satellite imager
MODIS (MODerate resolution Imaging Spectroradiometer) and the ground-based
sun photometer network AERONET (AErosol Robotic NETwork), and three different
global aerosol models, we compare annual and monthly averages of full model
data to sampled model data. Our results show that sampling errors as large as
100 % in AOT (aerosol optical thickness), 0.4 in AE (Ångström
Exponent) and 0.05 in SSA (single scattering albedo) are possible. Even in
daily averages, sampling errors can be significant. Moreover these sampling
errors are often correlated over long distances giving rise to artificial
contrasts between pristine and polluted events and regions. Additionally, we
provide evidence that suggests that models will underestimate these errors.
To prevent sampling errors, model data should be temporally collocated to the
observations before any analysis is made.
We also discuss how this work has consequences for in situ measurements (e.g.
aircraft campaigns or surface measurements) in model evaluation.
Although this study is framed in the context of model evaluation, it has a
clear and direct relevance to climatologies derived from observational
data sets.
Introduction
In the past decades, the role of atmospheric aerosol in the Earth's climate
and biosphere has become clearer. Aerosols can change the global radiation
budget directly and indirectly
. They can affect the temperature structure
of the atmosphere and may have consequences
for the hydrological cycle . Dust aerosols may transport
nutrients for the biosphere over long distances
and anthropogenic
aerosols can pose health hazards for humans
.
Yearly and zonal averages of AOT from the observations (MODIS-NRL
Aqua) and the models. The latter are averaged in two different ways: using
either all model data or only those sampled at the observation
times.
Global maps of yearly mean, standard deviation, and relative
standard deviation in AOT.
One approach to explore the role of aerosol is through (global) models. A
lot of effort has gone into evaluating global aerosol models against
observations
in the framework of the AEROCOM (AEROsol Comparisons between Observations and
Models) community (http://aerocom.met.no). Although this has allowed
the community to identify weaknesses in models (and has driven further model
development), less effort has gone into developing best practices when
performing such an evaluation.
When evaluating models with observations, one problem is the different
temporal sampling of the data sets. While models can in principle provide data
at any time, observations may not be available for much of a day or even
extended periods (up to several weeks) due to, e.g. satellite overpass times,
cloudiness, low-light conditions or other unfavourable circumstances as well
as instrument malfunction or maintenance. Although limited temporal sampling
is clearly an issue for remote-sensing data sets, in situ data may likewise be
affected. This temporal sampling issue is however ignored in many studies
where it is implicitly assumed that suitably long averaging periods (months
or years) will put model and observational data sets on equal footing.
In this paper, we will study errors due to temporal sampling errors by
applying temporal samplings from actual observational data sets to global
model data. The temporal evolution of aerosol has received some interest
before: used hourly nephelometer measurements of dry
extinction to study timescales of aerosol evolution over one polluted and
one remote site. They found timescales from 2 to 48 h, with aerosol often
becoming uncorrelated over a day and a half. used
AERONET (AErosol Robotic NETwork) AOT (Aerosol Optical Thickness) data to
assess whether a single daily overpass from either Terra or Aqua satellite
would allow an accurate estimate of daily-averaged AOT. They concluded this
was indeed possible, suggesting that aerosol diurnal cycles are small.
, also using AERONET AOT, showed that diurnal cycles of
10 to 40 % existed near polluted and biomass burning sources while diurnal
cycles were insignificant over ocean. put an upper limit
of 2.5 % on regional AOT changes over 3 hours by comparing MODIS
(MODerate resolution Imaging Spectroradiometer) Aqua and Terra aerosol
observations over the remote oceans. studied the
ability of MODIS Aqua and Terra to assess regional and monthly AOT using
model data and MODIS L2 temporal samplings. They found differences in
monthly, regional AOT of 0.01–0.02 over ocean and of 0.03–0.09 over land.
The model data consisted of daily averages so no investigation of diurnal cycles was possible.
The previous studies highlight aspects of the temporal evolution of aerosol
but always with the purpose of deriving climatologies from observational
data sets. Temporal sampling of aerosol observations in the context of model
evaluation has received little interest, although pointed
out that differences in AOT of up to 0.1 in monthly and annual regional
averages were possible when comparing model data to AATSR (Advanced
Along-Track Scanning Radiometer) satellite observations.
Global models are routinely compared to a host of remote-sensing data, from
satellites and ground sites. Within AEROCOM, standard practice is to use
daily averaged model data in these comparisons but in the literature monthly
or yearly averages are used as well. With regard to temporal sampling issues,
it seems that many questions are still left unanswered: what magnitude of
temporal sampling error is possible on daily, monthly and yearly timescales,
for individual grid points? Do these errors exhibit distinct spatial
patterns? Do aerosol diurnal cycles impact temporal sampling errors? Can
models represent aerosol temporal variability well enough to be used to
assess sampling errors? Are intensive aerosol properties like AE
(Ångström Exponent) and SSA (single scattering albedo) less affected
than extensive aerosol properties like AOT? What controls the size of these
sampling errors? And finally, how do temporal sampling errors compare to
model errors and observational errors? In this paper, we make a first attempt
at answering these questions.
In Sect. , we give a brief overview of the models that will
be used, followed by a similarly brief overview of the observational data sets
in Sect. . Our methodology is explained in more detail
in Sect. , but the bulk of our paper is dedicated to the
results in Sect. . We will start by describing simulated
observations, their temporal variability and how they compare to actual
observations in Sect. . Next, we will discuss the spatial
patterns in temporal sampling errors. A fuller explanation of what controls
temporal sampling errors is given in Sect. . These errors are
compared to observational errors and models errors in
Sect. . The paper is wrapped up with a summary
(Sect. ) of our results.
Models
Three global aerosol models, ECHAM-HAM, HadGEM-UKCA and MIROC-SPRINTARS, see
also Table , are used in this paper to provide time-varying
aerosol fields.
AOT time series and its associated power spectrum at 75∘ W,
0∘ N in HadGEM-UKCA. For this power spectrum, the ratio of power at
1 day over total power is ∼ 0.01. The straight line in the lower plot
has a slope of -5/3.
The global aerosol model ECHAM-HAM consists of the aerosol module HAM
coupled to the atmospheric general
circulation model ECHAM . It solves the
prognostic equations for vorticity, divergence, surface pressure and
temperature using spherical harmonics with triangular truncation. Aerosols
are advected with a flux-form semi-Lagrangian transport scheme
on a Gaussian grid. The aerosol module HAM calculates the
global evolution of five aerosol species: sulphate, particulate organic
matter, black carbon, sea salt and dust. These species are the constituents
of both internally and externally mixed aerosol particles whose size
distribution is represented by seven uni-modal log-normal distributions called
modes. These seven modes describe four size classes (nucleation, Aitken,
accumulation and coarse) and two hygroscopic classes (hydrophobic and
hydrophilic). HAM uses the two-moment M7 aerosol microphysics scheme
.
Global maps of the relative importance of the diurnal cycle: the
ratio of power at a period of 1 day to total power for AOT
time series.
Taylor plots showing the standard deviation and correlation of
modelled AOT against MODIS-NRL and AERONET observations. The dark grey
symbols refer to observations randomly perturbed with estimated observational
errors.
Median ratio of daily AOT variation
δo/δm across all AERONET sites. Only sites
with more than two observations for at least 24 days during 3 months were
used. Since the estimated error in AERONET AOT measurements is 0.01, the
error in measured δo can be no more than 2×0.012.
The global aerosol model HadGEM-UKCA uses the UKCA
aerosol and chemistry schemes with the third generation of the Hadley Centre
Global Environmental Model developed at the UK Met
Office. This circulation model is non-hydrostatic and uses a semi-Lagrangian
transport scheme. UKCA calculates the evolution of five aerosol species,
sulphate, particulate organic matter, black carbon, sea salt and dust, in
both internally and externally mixed particles. The aerosol scheme in UKCA is
based on the Global Model of Aerosol Processes (GLOMAP-mode,
) which is similar to the M7 framework. The main exception
is that dust is currently calculated separately using six size bins. UKCA hence
only considers five modes.
The global aerosol model MIROC-SPRINTARS uses the aerosol module SPRINTARS
in conjunction with the
atmospheric general circulation model MIROC. SPRINTARS calculates the global
evolution of three externally mixed aerosol species: sulphate, sea salt and
dust; and two species that can be either internally or externally mixed:
organic matter and black carbon. In contrast to HAM and UKCA, SPRINTARS uses
a single moment scheme and carries only mass as a prognostic variable. The
size distributions of sulphate, organic matter and black carbon are fixed but
for sea salt and dust a bin scheme is used.
All three models were run for the year 2007, with nudged meteorology,
prescribed sea surface temperatures and appropriate emission inventories (see
Table ).
Observations
We used the temporal sampling from several remote-sensing data sets, both
satellite and ground sites. The satellite sensor is the MODIS wide-swath
(∼2330 km) multi-channel imager onboard the Aqua satellite (local
equator crossing time 1:30 p.m., repeated view period: 1 to 2 days depending
on latitude). The ground sites constitute the AERONET network of
sun-photometers that measure solar transmittance with nominally a
15 min time resolution.
We chose not to use the original observations but data sets that have
undergone further quality checks and spatio-temporal aggregation. It seems
reasonable to study temporal sampling issues for data sets that have been
optimised for actual model evaluations.
The satellite remote-sensing data are the MODIS Aqua L3 NRL (Naval Research
Laboratory) data for 2007. These are
based on official MODIS Aqua L2 Coll. 5 data (see for a
discussion of the very similar over-ocean retrieval for Coll. 4 and
for Coll. 5 over-land retrievals) that have been subjected
to further quality checks, empirical corrections and spatial aggregation. The
data comprise of AOT and its error estimate for 1∘ by
1∘ grid boxes at a 6-hourly resolution. We have analysed MODIS
Terra as well but since it does not alter our conclusions, MODIS Terra
observations will not be used in this paper.
We also use the MODIS Aqua L3 AORI (Atmosphere and Ocean Research Institute)
data for 2007. These are based on MODIS Aqua L2 data
that have been subjected to further quality checks, empirical corrections and
spatial aggregation. The AORI data differ from the NRL data as they use
different empirical corrections and include both AOT and AE. Unlike the NRL
data, AORI data are available only over ocean. In a preliminary analysis
against Maritime Aerosol Network observations, we found that the AORI data
suffered less from the high bias in AOT at low AOT values than the NRL data.
The AORI AOT and AE data and its error estimates are available for
1∘ by 1∘ grid boxes at a 6-hourly resolution. MODIS
Terra data will be ignored, again because it does not alter our conclusions.
Not applying the extra quality checks in the AORI product almost doubles the
number of observations. While this does reduce the temporal sampling error
somewhat (primarily in yearly averages), it does not alter our conclusions
fundamentally. This also suggests that using Coll. 6 instead of Coll. 5 will
have a minimal impact.
The other two remote-sensing data sets are ground-based: AERONET Direct Sun
lev 2.0 and AERONET Version 2
Inversions lev 2.0 for 2007. Observations
at each site were averaged over 6 h, each 6 h. AERONET data used in this
study are AOT, AE and SSA.
As the MODIS-NRL product is provided on a regular 6-hourly grid, all other
observations were similarly put on a regular 6-hourly grid. Using a 3-hourly
grid for AERONET hardly affected our results. Moreover it was just as likely
to (slightly) increase sampling errors as (slightly) decrease them.
Median ratio of daily difference in maximum and minimum AOT
δo/δm, either observed or modelled, for all
AERONET sites. Smaller circles indicate sites where 0.5≤median δo/δm≤2. Only sites with more than two
observations per day for at least 24 days during 3 or more separate months
were used.
Top panel shows the 2007 yearly mean AOT of MODIS-NRL Aqua. Bottom
panel shows the temporal coverage (%) of observations during that year. Grey
colours indicate no observations available at all.
Method
The 3-hourly model data were linearly interpolated to the locations of actual
observations. These model values v were then sampled at the times of the
actual observations to generate simulated observations.
The straight average
v‾=N-1∑i=1i=Nvi,
(where i represents time and N the number of values over a day, a month or a year) is the average normally produced by models and often used in model evaluations.
The sampled average
ṽ=∑i=1i=Nfi-1∑i=1i=Nfivi,
is a model-simulated observation (daily, monthly or yearly mean) where fi represent the observational sampling (taken from actual observational data sets):
fi=0if no observation present at timei1if observation present at timei
The impact of not collocating model data with observations is now given by the error
ϵ=v‾-ṽ,
where we consider ṽ the reference value. After all, actual observations are (hopefully) a proxy for the truth and used to assess models. Note that this error can be rewritten as
ϵ=N-1∑i=1i=N1-∑j=1j=NfjN-1fivi.
The temporal sampling error depends on the statistics of the time series
vi as well as the statistics of observations times fi and in particular
the amount of observational temporal coverage
C=∑j=1j=NfjN.
ResultsDoes temporal sampling matter?
Figure shows yearly and zonally averaged AOT from
both observations (MODIS-NRL Aqua) and models (either collocated with the
observations or not). The difference between the straight model average
(solid red line) and the sampled model average (dotted red line) shows the
impact sampling has on model averages. The difference between the sampled
model average (dotted red line) and observations (dotted black line) is due
to model errors (and observational errors). Clearly, sampling errors can be
as big as model errors. We also see that resampling the model improves
agreement with some prominent features in the observations.
Top row shows global map of yearly mean of model AOT collocated with
MODIS-NRL Aqua AOT data. Bottom row shows the relative temporal sampling
error using MODIS-NRL Aqua AOT sampling. Grey colors indicate no observations
available.
Global map of absolute temporal sampling error using MODIS-AORI Aqua AE sampling. Grey colors indicate no observations available.
Temporal evolution of modelled AOT
To better understand the temporal sampling errors, we first need to consider
the models' temporal evolution. Figure shows the
mean, standard deviation and their ratio (relative standard deviation) of the
modelled AOT time series. All three models agree in global mean AOT patterns
(elevated AOT near natural sources like the Sahara and Southern Ocean and
anthropogenic sources like Europe and East Asia), but there are substantial
differences: HadGEM-UKCA shows lower mean AOT over the Sahara, ECHAM-HAM
shows lower AOT over Europe and MIROC-SPRINTARS shows lower AOT over the
Southern Ocean. Similarly, there are differences in standard deviation:
HadGEM-UKCA has its largest standard deviation in AOT over East-Asia,
ECHAM-HAM over the Sahara and East-Asia and MIROC-SPRINTARS over East-Asia
and Eastern Europe. The relative standard deviation (standard deviation
divided by the mean) also differs among these models, even though all three
had their meteorology nudged to reanalysis data, suggesting there are
fundamental differences in their time evolution due to the aerosol modelling
itself. In particular, HadGEM-UKCA shows globally lower relative standard
deviation than the other two models, while ECHAM-HAM and MIROC-SPRINTARS
differ in the spatial patterns of the relative standard deviation.
Regionally, relative standard deviation can easily differ by more than a
factor of 2 among these three models.
AOT time series in our models are characterised by power-law power spectra
with an exponent close to Kolmogorov's -5/3 constant, see
Fig. as an example. Sometimes this power spectrum
flattens out into white noise at large periods due to synoptic-scale weather
systems. In any case, AOT variability is largest for the longest periods.
Diurnal cycles are not very strong for these models and their global patterns
and magnitudes are very different (Fig. ). As the
modelled diurnal cycles are quite uncertain, so will our (later) conclusions
regarding diurnal sampling errors.
We present a comparison of the (collocated) models against actual AOT
observations as Taylor plots in Fig. . A Taylor plot
graphically represents the variability of the model data
and its correlation with observations and is especially suited to analyse the
models' temporal evolution. Here we show them for four different regions: the
entire Earth, the Amazon, East Asia and Western Africa. Mostly the models
underestimate observed variability (the exception is MIROC-SPRINTARS which
often overestimates it). Note that observational error has only a small
impact on these statistics.
Absolute temporal sampling error for monthly mean AOT using AERONET
sampling, as a function of time series standard deviation and observational
coverage. The grey boxes in the background (axis on the right), show the 25
and 75 % quantiles of those errors for equally sized
sub-samples.
Absolute temporal sampling error for monthly mean AE and SSA using
AERONET sampling, as a function of time series standard deviation and
observational coverage. The grey boxes in the background (axis on the right),
show the 25 and 75 % quantiles of those errors for equally sized
sub-samples.
Box-whisker plots of temporal sampling errors, observational and
model errors. For MODIS Aqua, sampling errors (blue), observational errors
(grey) and model errors (red) are shown side by side as a function of
averaging period (yearly, monthly, daily). The box-whisker plot shows the 2,
9, 25, 50, 75, 91 and 98 % quantiles of these errors, the dot shows the
mean error. The grey shading shows the 9, 25, 75 and 91 % quantiles of the
observational errors. The red numbers above each blue box-whisker show how
the different quantile ranges (from top to bottom: 2–98, 9–91 and
25–75 %) compare between the sampling error and the model
errors.
Correlation between model AOT at the time of MODIS-NRL Aqua
observation and a 24 h model AOT average. Top: 24 h model average uses
overpass time as the centre for the 24 h average; bottom: 24 h average
defined according to UTC. Note how in the bottom plot, correlations drop off
towards the date-line.
Ratio of the RMS (root mean squared) temporal sampling daily error
to RMS model daily error, i.c. MODIS-NRL Aqua. The daily errors were defined
according to UTC. The thin black contour represents a ratio of
0.3.
Relative temporal sampling error using MODIS-NRL Aqua AOT sampling.
The yearly averages are constructed from daily data, excluding days for which
no observations were present. This figure can be compared to the bottom row
of Fig. (but note that the colour bar has half
its range). Grey colors indicate no observations
available.
Box-whisker plots of temporal sampling errors, observational and
model errors. For AERONET, sampling errors (blue), observational errors
(grey) and model errors (red) are shown side by side as a function of
averaging period (yearly, monthly, daily). The box-whisker plot shows the 2,
9, 25, 50, 75, 91 and 98 % quantiles of these errors, the dot shows the
mean error. The grey shading shows the 9, 25, 75 and 91 % quantiles of the
observational errors. The red numbers above each blue box-whisker show how
the different quantile ranges (from top to bottom: 2–98, 9–91 and
25–75 %) compare between the sampling error and the model errors. For SSA,
no observational error estimates were
available.
Assessing the model's diurnal cycle from remote-sensing observations that
require daylight is difficult, but a simple analysis that is appropriate to
this paper's focus is to consider daily variation. This daily variation is
not necessarily the result of a diurnal cycle but may also be caused by, e.g.
synoptic weather patterns. We compare the difference δ between maximum
and minimum AOT over a day for all AERONET sites for both observations
δo and models δm. Figure
shows the median δo/δm for each AERONET site
throughout the year, while Table presents the median
across all sites (in this case, medians provide a more conservative and lower
estimate than means). Over a period of a day, observations tend to show more
variability than the models. Various sensitivity studies (e.g.
δo/δm as a function of δo as
shown in Table ) suggest that this is not due to
observational error. It is likely due to at least two factors: first an
underestimation of modelled AOT over the continents that limits absolute
daily variation; secondly, modelled AOT time series show very strong
auto-correlations (>0.8) over 6 h, further reducing potential daily
variation. Consequently, we suggest that these models underestimate daily
variation in AOT.
Similarly, there are substantial differences in the time series of AE and SSA
among the three models (not shown). In particular, ECHAM-HAM shows a larger
standard deviation in AE and SSA over the continents than the other two
models, while HadGEM-UKCA shows a very small standard deviation in SSA over
the oceans.
Spatial patterns in temporal sampling errors
Yearly averaged MODIS-NRL Aqua AOT and its temporal coverage are shown in
Fig. . Coverage is especially low over regions with high
cloudiness and land areas with strong variations in surface albedo. In
Fig. , we show yearly averages of the modelled
AOT collocated with MODIS-NRL Aqua. The relative sampling error
(Eq. ) when using straight model averages is also shown. There
are several things to note. First, temporal sampling errors can easily cause
AOT to be over or under-estimated by as much as 50 %. Secondly, these
temporal sampling errors show substantial spatial correlation: entire regions
show similar errors greatly reducing the possibility of reducing temporal
sampling errors through spatial averaging (see, e.g.
Fig. ). Thirdly, different models predict different
error patterns. Finally, we point out that observational coverage only partly
explains sampling errors. For instance, Fig. suggests
that India is far better sampled (temporally) than the Bay of Bengal, yet
relative errors are larger in India, at least in the ECHAM-HAM and
MIROC-SPRINTARS experiments.
Obviously, the temporal sampling error in yearly averages may be strongly
impacted by several months of no observations at all. Over land, snow cover
(combined with cloud cover) may preclude meaningful observations and, e.g. Siberia is not observed at all during the Northern Hemisphere winter. Even
over ocean, high latitudes may not be observed during part of the year due to
low SZA (Solar Zenith Angle) or ice cover. We have inspected global maps of
this temporal sampling error for monthly means, but found that errors can be
just as large as for yearly means, due to the 1 to 2-day period between
repeated views by MODIS and the possibility of extended cloud cover. In
particular, for almost every location on Earth observed by MODIS, we found at
least 1 month when temporal sampling errors exceeded 100 %. A more
in-depth analysis of the impact of averaging periods will follow later
(Sect. ).
Lastly, the absolute temporal sampling error in yearly averaged AE from the
MODIS-AORI data set is shown in Fig. . The
observational coverage of AE is less than that of AOT, due to more stringent
quality checks (not shown). Sampling errors rarely exceed ±0.3. However,
a very distinct spatial pattern can be seen for all three models: near
coast-lines, especially in polluted outflow regions, the error tends to be
strongly negative while over the remote oceans it tends to be strongly
positive. If one does not properly collocate AE model data with observations,
this would create an artificial contrast up to ∼ 0.6 in AE between the
continents and the remote oceans. The reason is that AE observations require
a minimum AOT to be successful (see ). In areas with
polluted outflows, low AOT correspond to the sea-salt background with low AE
and observations will mostly sample the outflow with high AE, leading to
negative sampling errors. Conversely, over the remote oceans high wind-speeds
lead to high AOT and low AE (larger particles) that will be more often
observed than the lower AOT and higher AE (smaller particles) that occur at
low wind-speeds.
The last paragraph suggests that minimum AOT requirements in retrievals can
have large impacts on temporal sampling errors. While this was shown for the
AORI data set, already the official MODIS Coll. 5 product shows a strong
dependence of the quality of AE retrievals on AOT values, as might be
expected. See also Fig. 11 in .
Drivers of temporal sampling errors
In Fig. , we show temporal sampling errors for
monthly averaged AERONET AOT (similar plots can be shown for MODIS). Sampling
errors increase with the standard deviation of the time series, but decrease
with increasing observational temporal coverage. Still, even for relatively
high coverage large sampling errors are possible. We surmise that the clear
positive bias is due to cases of high relative humidity that will tend to (1) prevent observations due to cloudiness; (2) increase model AOT due to wet
growth. Randomising the observation times (instead of using actual AERONET
times) in this analysis removes this bias and also reduces the spread in the
errors by 15 to 45 % (depending on the model). Thus it appears that
correlations between the time series and the observation times (see
Eq. ) also affect these sampling errors.
Similar figures for monthly-averaged AERONET AE and SSA are shown in
Fig. . They confirm previous results and
mostly serve to show the magnitude of the sampling errors that can possibly
occur. The positive bias for SSA is likely due to a minimum AOT in the
AERONET Inversion data files (all inverted SSA values have AOT ≥ 0.2).
As a result, the sampled model data will mostly sample pollution or dust
events with low SSA while the straight model data also include the aerosol
background state with higher SSA.
Temporal sampling errors in context
To put these sampling errors in context, we will compare them to model errors
and observational errors. The model errors are defined as the difference of
collocated model values from actual observations. Strictly speaking this
“model error” includes observational errors as well but unfortunately they
can not be separated. However, estimates of this observational error's
standard deviation are part of our observational data sets (we will assume
this error distribution to be an unbiased Gaussian). The model error (minus
the observational error) is the signal we are interested in when evaluating
models.
Figure shows a comparison of the above errors
for yearly, monthly and daily averages of MODIS data (AOT and AE). For both
AOT and AE, we see that observational errors and model errors decrease as
averaging periods increase. In contrast, sampling errors behave differently,
with the largest errors typically occurring for monthly averages and the
smallest errors for daily averages. The models differ both in the sampling
errors and how they compare to the model errors. But a few conclusions seem
obvious: (1) for yearly and monthly averages, sampling errors will contribute
considerably (typically 30–60 %) to model errors (defined as the
difference between a model and observations) if no collocation is performed;
(2) sampling errors in AOT are comparable to or larger than observational
errors for monthly or yearly averages; (3) for daily averages, these sampling
errors appear to be smaller.
This last point is important as standard practice for AEROCOM models is to
save data as daily averages. Doing so would incur sampling errors of at most
25 % of the model error. There are a few caveats however. We have already
pointed out that models seem to under-estimate AOT variability, especially on
daily timescales (see Sect. ). Thus we are likely to
underestimate daily sampling errors. Furthermore, the AEROCOM daily averages
are defined according to UTC. This means that, e.g. satellite observations
(made close to local noon time) near the date-line are not as representative
of the model day as observations near the Greenwich meridian. The consequence
of this is shown in Fig. , where correlations between
daily model averages and simulated observations clearly drop off towards the
date-line. A box-whisker plot as in Fig. also
hides the fact that in large parts of the world daily sampling errors are
in magnitude at least 30 % of the daily model errors (see
Fig. ).
It is interesting to consider what temporal sampling errors remain if an
annual average is constructed from daily model averages and observations,
excluding those days for which no observations exist.
Figure shows that this does indeed
reduce sampling errors compared to the case of straight annual averages (as
in Fig. ) but we still find typical root mean
square errors of 12, 7 and 17 % for ECHAM-HAM, HadGEM-UKCA and
MIROC-SPRINTARS. Interestingly, such a procedure results in mostly positive
errors because daily minimum AOT (as modelled) occurs near the time of
observation. Note also that the error patterns correlate somewhat with the
diurnal cycles in these models, see Fig. .
Any analysis of model data attempting to look at shorter timescales (e.g.
scatter plots, time series) will be further negatively affected when using
daily data. To prevent this, models need to be resampled to the observation
times.
Figure shows a comparison of the above errors
for yearly, monthly and daily averages of AERONET data (AOT, AE and SSA). The
overall picture is much the same as Fig. : model
errors and observational errors decrease as averaging increases, while
sampling errors are the largest for either yearly or monthly averages. Note
that in the case of AERONET AOT, already for daily averages, sampling errors
are larger than observational errors.
Summary
Although model data and observations usually have very different temporal
sampling, researchers often assume this does not affect their analyses.
Consequently, monthly or yearly means are compared without first temporally
collocating the model data with the observations. We have assessed potential
errors resulting from this practice and shown them to be significant. We would
like to point out that the practice of temporal collocation of data sets is
very normal in the remote-sensing and data assimilation communities, but less
so in the modelling community.
Our analysis is based on the temporal sampling of several oft used remote-sensing data sets (MODIS, AERONET) and data from three different models:
ECHAM-HAM, HadGEM-UKCA and MIROC-SPRINTARS. We define the temporal sampling
error as the difference in yearly, monthly or daily means of the full model
data set and the sampled model data sets. Three different models were used as
we found that current models differ in their temporal evolution even though
yearly mean global patterns are fairly similar and meteorological fields were
nudged to reanalysis data. Although this study is framed in the context of
model evaluation, it has a clear and direct relevance to climatologies
derived from observational data sets.
We find that temporal sampling errors in yearly and monthly means can amount
to 100 % in AOT, 0.4 in AE and 0.05 in SSA. In addition, these sampling
errors are comparable to model errors (30–60 % for MODIS, 20–90 % for
AERONET). While daily averages incur smaller sampling errors, we argue (based
on observations) that our models very likely underestimate daily variation
and hence sampling errors. In addition, model daily averages are defined
through UTC while remote-sensing observations are only possible during local
daylight. This introduces a marked longitudinal dependence in temporal
sampling errors. Annual averages constructed from daily averages still
exhibit temporal sampling errors although at reduced levels (we estimate
typical errors of 7–17 %).
Temporal sampling errors will affect model evaluation of not only AOT, AE and
SSA but also derived properties like direct aerosol radiative forcing, if
data are not properly collocated with the observations. Our analysis should
also provide caution to researchers using in situ data from, e.g. ground
sites. While such data often have nominally high measurement frequencies
(hours), significant gaps (days to weeks) in temporal coverage may be
present. Much will depend on the observational sampling and the nature of the
observed time series. For instance, PM2.5 filter measurements by EMEP
(European Monitoring and Evaluation Network, http://www.emep.int) are
time-integrated measurements that can probably be compared to models without
temporal sampling issues. But several EUSAAR (European Supersites for
Atmospheric Aerosol Research, http://www.eusaar.net) stations have
significant intermittency in their observations. Flight campaign data
obviously require temporal collocation to make any sense in a model
evaluation context. Also, unlike remotely sensed column properties like AOT,
in situ measurements will be affected by vertical transport. This may
possibly exacerbate any temporal sampling issues.
As a corollary to our study, we have shown that the temporal evolution of
models can be very different (although yearly means are quite similar). We
suggest that more effort should be made to understand modelled and observed
time series. It is likely that such time series contain finger prints of
individual aerosol processes and provide new ways to evaluate models. In
particular we point out the large differences we found in diurnal cycles (see
Fig. ) and the research opportunities that may lie in
observational data sets (e.g. from geostationary satellites) that resolve this
diurnal cycle.
Finally, if there is one error in the field of aerosol modelling over which
we have direct control and that can be confidently eliminated, it is the
error due to incongruous temporal sampling of model data and observations.
Not doing so barely saves time or resources but risks compromising any model
evaluation. For instance, we have shown that the latitudinal pattern of
yearly, zonal averages of collocated model AOT agrees better with MODIS
observations than the normal yearly, zonal model average. The collocation of
model data with observations can either be done on-line through observation
simulators or off-line through sampling of high frequency model output. A
generic tool to support the latter operation is freely available as the
Community Intercomparison Suite (http://www.cistools.net).
Acknowledgements
This work was supported by the Natural Environmental Research Council grant
nr NE/J024252/1 (Global Aerosol Synthesis And Science Project). Computational
resources for the ECHAM-HAM runs were made available by Deutsches
Klimarechenzentrum (DKRZ) through support from the Bundesministerium für
Bildung und Forschung (BMBF). The ECHAM-HAMMOZ model is developed by a
consortium composed of ETH Zurich, Max Planck Institut für Meteorologie,
Forschungszentrum Jülich, University of Oxford, the Finnish
Meteorological Institute and the Leibniz Institute for Tropospheric Research,
and managed by the Center for Climate Systems Modeling (C2SM) at ETH Zurich.
P. Stier would like to acknowledge funding from the European Research
Council under the European Union's Seventh Framework Programme
(FP7/2007-2013) ERC project ACCLAIM (grant agreement no. FP7-280025).
HadGEM-UKCA was run on the ARCHER UK National Supercomputing Service
(http://www.archer.ac.uk). The development of the UKCA model
(www.ukca.ac.uk) was supported by the UK's Natural Environment Research
Council (NERC) through the NERC Centres for Atmospheric Science (NCAS)
initiative. MIROC-SPRINTARS was run on the SX-9 supercomputer at NIES (CGER)
in Japan. The figures in this paper were prepared using David W. Fanning's
coyote library for IDL. The authors thank an anonymous reviewer and in
particular Andrew Sayer for useful comments that helped improve the
manuscript.Edited by: K. Tsigaridis
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