Data assimilation systems allow for estimating surface fluxes of
greenhouse gases from atmospheric concentration measurements. Good
knowledge about fluxes is essential to understand how climate change
affects ecosystems and to characterize feedback mechanisms. Based
on the assimilation of more than 1 year of atmospheric in situ
concentration measurements, we compare the performance of two
established data assimilation models, CarbonTracker and TM5-4DVar (Transport Model 5 – Four-Dimensional Variational model),
for CO
Our results show that both models provide optimized CO
Sources and sinks of atmospheric carbon dioxide (
Inverse modeling therefore uses
There are two main classes of assimilation techniques for complex
inversions, variational methods and ensemble methods
The performance of ensemble methods and variational methods has been
evaluated previously for numerical weather prediction
Here, we focus on evaluating the performance of an ensemble method and
a variational method used for real atmospheric
Besides the mathematical treatment of the inversion, CarbonTracker and
TM5-4DVar differ in the design of the state vector. CarbonTracker
optimizes fluxes binned by regions with similar vegetation – like
cropland or boreal forest – and separated by geographic regions
following the Transcom basemap
Both methods are used in a number of studies. CarbonTracker studies
include estimates of global
Our goal is to evaluate the impact of the inverse method (including
the flux representation) on the estimated surface
fluxes. Therefore, we must make sure that the other components of the
DA systems – the observations to be assimilated, the transport model
and the prior assumptions – are the same. After a short summary of
the general CarbonTracker and TM5-4DVar methodology in
Sect.
The DA systems aim at inferring a state vector
In general, minimization of Eq. (
While theoretically the minimization of Eq. (
CarbonTracker is an inverse modeling framework based on the ensemble
square root filter (EnSRF) developed by
Commonly, a gain matrix
To estimate the gain matrix
Then, the terms
CarbonTracker uses a refined approach for stepping through the entire
time period considered. CarbonTracker's state vector
The spatial binning of CarbonTracker's state vector follows the
Transcom regions CarbonTracker 2011_oi results
and documentation are provided by NOAA ESRL, Boulder, Colorado, USA,
from the website
The structure of the background covariance
The version of CarbonTracker used here is derived from version 1.0 of
the code maintained by Wageningen University with the same state
vector as CarbonTracker North America
Whereas the EnSRF in CarbonTracker reduces the dimension of the
minimization problem of Eq. (
TM5-4DVar's state vector
Given the setup of the CarbonTracker and TM5-4DVar modeling systems,
we aim at comparing the performance of their data assimilation
concepts for the purpose of
To connect concentration measurements and surface fluxes,
CarbonTracker and TM5-4DVar use a transport model which transports the
CarbonTracker and TM5-4DVar use the same background fluxes and initial
concentration fields. The biosphere fluxes are taken from the Simple
Biosphere model using the Carnegie–Ames–Stanford Approach
The initial concentration field is generated from the output of
a previous CarbonTracker run which ended on 1 January 2007. The field
for 2009 is derived by increasing the concentration by 1.9 parts per
million (
The covariance of the fluxes is defined in the models as described in
Sects.
Both DA systems use the same observations from the obspack
compilation of in situ
Additionally we take out five sites which have more than 1000 measurements in the assimilation period. This is to keep the TM5-4DVar results representative of TM5-4DVar runs which use the native TM5-4DVar input. When using these five sites with the CarbonTracker preprocessing, TM5-4DVar shows strong gradients between neighboring grid cells in North America which it does not show when processing its native set of observations. In addition to these 26 excluded sites, there are 24 further sites from which the default run of CarbonTracker uses no data or only a subset of the observations. The reasons for not using some of the observation data of a site include that the data is assumed not representative of its grid cell or recorded in aircraft campaigns.
Measurement uncertainty is set to a fixed value for each site
accounting for the measurement errors and for representativeness
errors. The latter originate from using the in situ samples to
represent the
Yearly global
As a first step, we compare and validate the performance of
CarbonTracker and TM5-4DVar by evaluating the difference between
measured and modeled
As an example for an assimilated site, Fig.
Time series of measured and modeled
Histograms of the mismatch between measured and modeled
The mismatch between measured and modeled
Time series of measured and modeled
The concentrations from the prior forward run in
Fig.
Histograms of the mismatch between measured and modeled
Model–measurement bias of TM5-4DVar against CarbonTracker for
non-assimilated measurement sites. Each symbol corresponds to a case
resampling exercise where the biases are calculated for 25 randomly
drawn sites out of the total 50 resampling sites listed in Table S1
in the Supplement. The baseline run
(dots) is compared to a CarbonTracker run with the assimilation
period extended to
Time series of measured and modeled
The histograms for a posteriori CarbonTracker and TM5-4DVar concentrations reveal some non-Gaussian behavior, with long tails toward greater mismatch and with a narrow peak at the center. The tails most likely stem from temporally varying contributions to the representativeness error which our input data assumes constant in time. The narrow peak likely stems from two sources: first, sites with high-frequency measurements are assumed uncorrelated in the models and as such provide a stronger constraint than sites with low-frequency measurements. Second, an already well-optimized prior which is close to the observations causes the models to stick to the prior in a sparse observation network.
In summary, both models show similar performance for assimilated sites, and the assimilation substantially reduces the mismatch between modeled and measured concentrations at assimilated sites.
Global fluxes from the baseline runs of TM5-4DVar and CarbonTracker. The Prior is shown in the binning from CarbonTracker. The uncertainties shown for CarbonTracker are aggregated spatially but not temporally. As such they represent the uncertainty of the estimated fluxes, calculated directly from the ensemble. These uncertainties are excluded from the annually aggregated graphs, because there is no method for temporally aggregating the uncertainties in a way which is comparable to the uncertainties estimated by TM5-4DVar.
Next, we evaluate the performance of the DA systems for sites whose
observations are not assimilated. These sites provide
independent validation of the results. Figure
Fluxes from TM5-4DVar and CarbonTracker aggregated on
continental scale. The uncertainties for TM5-4DVar are calculated
following
The histograms of model–observation mismatch, are shown in
Fig.
A posteriori CarbonTracker concentrations show a larger bias for
non-assimilated measurements (0.097) than for assimilated
measurements (0.006). TM5-4DVar biases are more similar for
non-assimilated (0.004) and assimilated measurements (0.025). In
order to investigate whether these differences are likely to be an
artefact of our selection of validation sites, we conduct a resampling
experiment. Out of the 50 sites for which there are non-assimilated
observations – our 26 validation sites, aircraft measurements and
sites for which only a given measurement method is assimilated – we
randomly select subsets of 25 sites and recalculate the statistical
model–observation bias for non-assimilated measurements. Then we
repeat the exercise 9 times and examine the distribution of the
resampled CarbonTracker and TM5-4DVar
biases. Figure
So, while a posteriori CarbonTracker concentrations appear offset from the (non-assimilated) observations, TM5-4DVar does not show a significant overall bias but does show greater station-to-station variability for the model–observation mismatch.
In order to investigate whether the robust bias our resampling found for
CarbonTracker can be due to the choice of the EnSRF assimilation time
window, we vary CarbonTracker's lag and cycle parameters.
Figure
Time series of
Section
As first step we describe the results of the baseline runs. Then we analyze detectable features and the effect of a longer assimilation window in CarbonTracker.
For the baseline CarbonTracker and TM5-4DVar runs,
Table
Different from the Monte Carlo-based uncertainty calculation which
Due to this we expect our
uncertainties to overestimate the real uncertainties from
measurement and representativeness errors. With this caveat, the sink
estimates of the two models are consistent within the TM5-4DVar
uncertainties and also match previous findings for CarbonTracker
Figure
The time series of South American surface fluxes in
Fig.
South America suffers from sparseness of observational constraints
such that validation of the estimated surface fluxes via comparison of
measured and modeled atmospheric
To check its impact on the fluxes, we perform a sensitivity run
without assimilating Arembepe. In this run both models are similarly
good at matching modeled a posteriori and measured
The aggregated fluxes in Fig.
The flux changes in CarbonTracker with assimilating Arembepe are within the
estimated uncertainties in the yearly aggregated fluxes and in the
time series. Disabling the outlier rejection in CarbonTracker causes the
modeled concentrations to follow the observations much more closely.
CarbonTracker specifies the flux uncertainty relative to the total flux,
which in April and May 2009 yields a lower uncertainty than that from
TM5-4DVar, which can cause the flux to change less than in TM5-4DVar in those
months, leading to the strong reaction of the outlier rejection. However, as shown
in Fig.
The fluxes induced by assimilating Arembepe show that TM5-4DVar is more susceptible than CarbonTracker to the effect of single measurement sites in regions with very low observation density.
Figure
The time series in Fig.
For a quantitative discussion of the propagation of aggregation errors
see
In summary we see good agreement for the baseline fluxes between CarbonTracker and TM5-4DVar on a global scale and for most continents and oceans. The mismatch of the fluxes in South America, the Indian Ocean and Asia can be traced back to two distinct effects: a different flux response in regions with very limited observation coverage and using weekly (CarbonTracker) or monthly (TM5-4DVar) adjustments to account for mismatches on shorter timescales.
In order to assess the importance of data density and coverage on the
two DA systems, we follow the approach which
Figure The 2013B release of the
estimated fluxes of CarbonTracker North America (NOAA, ESRL) is available
from
Globally aggregated surface fluxes estimated by the model runs indicated in the legend. In all aggregated flux bar charts, the uncertainties are estimated by TM5-4DVar.
Fluxes for CarbonTracker and TM5-4DVar from April 2009 to April 2010 separated into the two Transcom regions in North America.
Visualization of the weight of the measurement sites which are assimilated in North America in the respective runs.
On the continental scale we take a closer look at North America, since
changes in observation density are historically most pronounced
there. Figure
The stronger land sink seen by TM5-4DVar for 2/cont stems from
assimilating only two sites: a site in West Branch, Iowa, USA (WBI,
41.7
On the other hand, the overall North American sink of
0.65
The strong reduction of the uncertainty estimate in the North America fluxes of TM5-4DVar in the 2/cont run, despite assimilating only 2 sites in North America, shows the sensitivity of these estimates to the raw number of assimilated observations. It proves that the actual structure of the observational network has to be taken into account when interpreting the reduction of model-estimated uncertainty.
Overall our results show that the current observation coverage in North America allows estimating robust fluxes on continental scales and on the scales of Transcom regions. The improving agreement with increasing observation coverage between both models for the aggregated North American fluxes and the two Transcom regions in North America suggests that increasing the observation coverage allows obtaining robust fluxes on even smaller scales.
Our study evaluates the performance of the data assimilation models
CarbonTracker and TM5-4DVar by comparing their a posteriori
Both inverse models yield
The a posteriori fluxes from both models are in good agreement on
a global scale, but on continental scales they show significant
differences, most noticeably in South America which has very sparse
coverage of observation sites. Investigating the flux time series
allows tracing these differences back to spurious flux adjustments in
TM5-4DVar for South America due to assimilating observations from
a single site in Arembepe, Brazil, along with compensating fluxes in
the oceans. Also we see a difference in the adjustment of Asian
fluxes, but an additional CarbonTracker run with a coarser temporal
flux adjustment bin size of 20 days gives similar fluxes in Asia as
TM5-4DVar. Here, the flux time series reveal that part of the weaker
sink in CarbonTracker with smaller bin size stems from high-frequency
changes which cannot be represented with the monthly binning of
flux adaptations in TM5-4DVar and the CarbonTracker run with bins of
20 days. The impact of this effect on the fluxes in Asia is
0.5
To better analyze the sensitivity of both models to the observation
coverage, we run the models with collections of measurement sites
selected by historical availability. In North America, where the
change of observation coverage is most pronounced, fluxes estimated
with the observation network from 2000 differ by
0.25
TM5-4DVar has a stronger response to the data coverage than CarbonTracker. This shows that the ecoregion approach in CarbonTracker with its stronger meridional coupling of fluxes and observations makes CarbonTracker less susceptible to changes in the distribution and density of observations than the simple global flux covariance in TM5-4DVar. As such it might be useful to reuse CarbonTracker's spatial flux correlation structure in TM5-4DVar.
Generally, we see sensitivity of the optimized fluxes to the density and distribution of observations which might be particularly important for using satellite data, in which the coverage of observations changes with cloud cover. The improved agreement between both models when adding observation sites indicates that the coverage of observation sites in North America should be sufficient to yield robust fluxes on a continental scale when only considering the uncertainty from the inverse methods and the flux representation.
A. Butz and A. Babenhauserheide are supported by the
Emmy Noether program of the Deutsche Forschungsgemeinschaft (DFG)
through grant BU2599/1-1 (RemoteC). This study would not have been
possible without the work of Maarten Krol (SRON Netherlands
Institute for Space Research, Utrecht, the Netherlands; Institute
for Marine and Atmospheric Research (IMAU), Utrecht University,
Utrecht, the Netherlands; Department of Meteorology and Air Quality
(MAQ), Wageningen University and Research Centre, Wageningen, the
Netherlands), who maintains the Transport Model 5 (TM5). Also the
authors are indebted to the many individuals and institutions who
have contributed original data to the ObsPack project, specifically
version v1.0.2 2013-01-28 used in this study. They are
J. A. Morgui (IC3); Ernst Brunke (SAWS); Samuel Hammer (UHEI-IUP);
Shuji Aoki (NIPR); Markus Leuenberger (KUP);
Harro Meijer (RUG); Hidekazu Matsueda (NIES-MRI);
Juha Hatakka (FMI); Paul Krummel (CSIRO);
Marcel van der Schoot (CSIRO); Margaret Torn (LBNL);
Michel Ramonet (LSCE/RAMCES); Doug Worthy (EC);
Angel J. Gomez-Pelaez (AEMET); Takakiyo Nakazawa (NIPR);
Shinji Morimoto (NIPR); Luciana V. Gatti (IPEN); Ken Masarie (NOAA);
Arlyn Andrews (NOAA); Ray Langenfelds (CSIRO);
Sebastien Biraud (LBNL); Colm Sweeney (NOAA);
Britton Stephens (NCAR); Paul Steele (CSIRO); Ed Dlugokencky (NOAA);
Ralph Keeling (SIO); Eckhart Scheel (SAWS);
Toshinobu Machida (NIES-MRI); Tuula Aalto (FMI);
Hiroshi Koide (JMA); Steve Wofsy (HU);
Martina Schmidt (LSCE/RAMCES); Yousuke Sawa (NIES-MRI);
Laszlo Haszpra (HMS); Ingeborg Levin (UHEI-IUP);
Kirk Thoning (NOAA); Casper Labuschagne (SAWS) and
Pieter Tans (NOAA). Also we thank the staff of CarbonTracker NOAA ESRL,
Boulder, Colorado, USA, for providing the 2011_oi results and
documentation. Finally we thank