GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus PublicationsGöttingen, Germany10.5194/gmd-10-1-2017Improving the inter-hemispheric gradient of total column atmospheric
CO2 and CH4 in simulations with the ECMWF semi-Lagrangian atmospheric global modelAgusti-PanaredaAnnaanna.agusti-panareda@ecmwf.intDiamantakisMichailBayonaVictorKlappenbachFriedrichButzAndrehttps://orcid.org/0000-0003-0593-1608European Centre for Medium-Range Weather Forecasts, Reading, UKIMK-ASF, Karlsruhe Institute of Technology (KIT), Leopoldshafen, GermanyAnna Agusti-Panareda (anna.agusti-panareda@ecmwf.int)2January20171011182June201614July201628October201621November2016This 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://gmd.copernicus.org/articles/10/1/2017/gmd-10-1-2017.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/10/1/2017/gmd-10-1-2017.pdf
It is a widely established fact that standard semi-Lagrangian
advection schemes are highly efficient numerical techniques for simulating
the transport of atmospheric tracers. However, as they are not formally mass
conserving, it is essential to use some method for restoring mass
conservation in long time range forecasts. A common approach is to use global
mass fixers. This is the case of the semi-Lagrangian advection scheme in the
Integrated Forecasting System (IFS) model used by the Copernicus Atmosphere
Monitoring Service (CAMS) at the European Centre for Medium-Range Weather
Forecasts (ECMWF).
Mass fixers are algorithms with substantial differences in complexity and
sophistication but in general of low computational cost. This paper shows the
positive impact mass fixers have on the inter-hemispheric gradient of total
atmospheric column-averaged CO2 and CH4, a crucial feature of
their spatial distribution. Two algorithms are compared: the simple
“proportional” and the more complex Bermejo–Conde schemes. The former is
widely used by several Earth system climate models as well the CAMS global
forecasts and analysis of atmospheric composition, while the latter has been
recently implemented in IFS. Comparisons against total column observations
demonstrate that the proportional mass fixer is shown to be suitable for the
low-resolution simulations, but for the high-resolution simulations the
Bermejo–Conde scheme clearly gives better results. These results have
potential repercussions for climate Earth system models using proportional
mass fixers as their resolution increases. It also emphasises the importance
of benchmarking the tracer mass fixers with the inter-hemispheric gradient of
long-lived greenhouse gases using observations.
Introduction
The monitoring and prediction of climate change relies on accurately modelling
the long-lived greenhouse gases using Earth system models (ESMs)
e.g.. Carbon dioxide
(CO2) and methane (CH4) are the most important anthropogenic
greenhouse gases . Because of their relevance to
climate mitigation and policy making, they are
monitored using flux inversion systems based on atmospheric chemical transport models (CTMs)
e.g.. Complementing the climate monitoring,
global analyses and forecasts of CO2 and CH4 are also performed each day as part of
the Copernicus Atmosphere Monitoring Service (CAMS) at the European Centre
for Medium-Range Weather Forecasts (ECMWF) using the Integrated Forecasting System (IFS, www.ecmwf.int/en/forecasts/documentation-and-support/changes-ecmwf-model/ifs-documentation).
Both atmospheric CO2 and CH4 are characterised by a trend
associated with an annual growth rate, a seasonal cycle and an
inter-hemispheric gradient, which is consistent with the temporal and spatial
distribution of their sources and sinks, tropopause height and atmospheric
transport . In ESMs and CTMs the
transport is modelled using advection, convection and turbulent mixing
schemes based on numerical weather prediction (NWP) methods. The
semi-Lagrangian (SL) advection scheme is widely used in NWP (e.g. the ECMWF
IFS model, Environment Canada GEM model; ) and ESMs
e.g. ACCESS, HadGM2; documented by because of its high numerical stability,
accuracy and computational efficiency. Furthermore, for the problem of
multiple tracer advection, it is undeniably the most efficient approach given
that for each tracer the transport operation reduces to interpolating the
field from the fixed grid to the time-step-dependent departure point grid.
The latter is re-computed only once at each new time step, which implies that
the same interpolation weights can be used for all tracers (and prognostic
fields in general). However, the non-flux form of the SL scheme by default
does not conserve mass. This can lead to small errors in the global mass of
tracers when modelling the tracer advection. In the case of CH4 and
CO2, these errors accumulate with time because there is a slow or
non-existent chemical sink in the atmosphere. It is therefore imperative to
apply a mass fixer in order to restore the conservation of the total tracer
mass. This is particularly important for CO2, as the mass
conservation error can reach values that are as large as the observed global
mass trend resulting from their surface fluxes and can significantly distort
its large-scale distribution e.g.. There are
several methods to fix the global tracer mass, from the simple proportional
mass fixers to more sophisticated algorithms that focus the correction where
the conservation error associated with the tracer advection is assumed to be
largest, i.e. in the regions with strongest gradients. Because of its
simplicity, the proportional mass fixer is widely used by ESMs and NWP models
. There are different implementations of the global
proportional mass fixer. However, the correction procedure is very
homogeneous/uniform. For this reason, it is prone to the artificial transfer
of mass and long-range propagation of errors .
Therefore, it has the potential to create a distortion in the
inter-hemispheric gradient of tracers .
implemented and tested several of these
global mass fixers on the humidity, cloud fields and ozone in the IFS. Both
CO2 and CH4 have different characteristics and requirements
than shorter-lived reactive gases and humidity. Because of their long life,
they are generally well-mixed with smooth gradients, and large background
values relative to their gradients. Their large-scale spatial variability is
characterised by a relatively weak inter-hemispheric gradient (of the order
of 100 ppb or 5 % for CH4 and 10 ppm or 2.5 % for CO2).
Nevertheless, it constitutes a crucial feature to represent in the models
because it reflects the spatial distribution of the surface sources and/or sinks
. Considering these properties and
the computational cost, flexibility and efficiency, the
fixer is deemed to be the most suited among the
available schemes in the IFS for the modelling requirements of the long-lived
greenhouse gases. This is consistent with the recent tests performed with the
Environment Canada Semi-Lagrangian Model by and
.
This paper presents a comparison of a customised mass
fixer and the proportional mass fixer, which was operational until recently
in the CAMS CO2 and CH4 forecasting and analysis system
, and it is also widely used
in Earth system climate models . The impact of the two mass fixers on the preservation of the
CO2 and CH4 inter-hemispheric gradient is a crucial benchmark
for testing their suitability in any CO2 and CH4 forecasting
and analysis system. Furthermore, this study can provide valuable feedback to
the Earth system climate models using the simple global proportional mass
fixer. The impact of resolution on the mass conservation and performance of
the mass fixers can help guide the choice of mass fixer in future climate
simulations.
The structure the paper is as follows: in Sect. the mass
fixers are described; the experiments performed to test the impact of the
mass fixers are presented in Sect. ; the observations are
documented in Sect. ; the results from the experiments and their
evaluation using observations are provided in Sect. ; a
summary of the main findings is given in Sect. .
Global tracer mass fixers
The two tracer mass fixers selected in this study are described in this
section. The algorithms of these fixers are described in detail by
as part of a set available in the ECMWF IFS
model. Thus, their notation is used henceforth. A few minor modifications
have been necessary in order to fine-tune these algorithms for simulating the
transport of long-lived greenhouse gases. For example, it was found that,
given that a mass mixing ratio formulation is used, a small mass conservation
error in the total atmospheric mass after advection can lead to a systematic
accumulation of the tracer mass conservation error with time. This stems from
the fact that the global mass of a tracer is computed using surface pressure
(see Eq. 1 below), that the mass conservation error always has the same sign, and
finally that there are no atmospheric processes (e.g. strong chemical
sources and/or sinks) that can counter the effect of the systematic error
accumulation. It was therefore necessary to apply the mass fixer on surface
pressure as well, as explained in the paragraphs below.
The IFS is a hydrostatic model using a pressure-based coordinate system which
implies that the surface pressure field is required to compute the total
tracer mass. For example, the mass of a tracer χ with mass mixing ratio
ϕχ=ρχ/ρ, where ρχ, ρ the tracer and
air-density respectively, is given by
M(ϕχ,p)=∑j=1NAj∑k=1KϕjkΔpjkg,
where p is the atmospheric pressure field, Aj is the horizontal surface
area of box j, k is the vertical model level and g the gravitational
constant. Each model level consists of N grid points and there are K
vertical levels.
Experiments with IFS at different resolutions showed that it is important
that after the advection step and before the mass of the tracer is corrected,
the pressure field needs to be corrected in order to ensure that the total
mass of air
M(p)=∑j=1NAj∑k=1KΔpjkg
is globally conserved in the tracer mass computation. We did not find large
differences in the method of correction applied here, and this can be done
either by the proportional algorithm (described below) or by the McGregor
scheme described also in . The latter was
chosen as it gives realistic corrections of surface pressure in regions with
cyclonic activity or regions with orography and additionally has very low
computational cost. For a model using a height-based vertical coordinate
system and density as the prognostic variable, the correction should be
applied on density. In the following sections, the pressure after the SL
advection is always corrected to have the same global value as before
advection by using the proportional fixer presented below.
List of simulations at different resolutions and with different mass fixers performed from 1 March 2013 to 30 April 2014.
Experiment descriptionModel grid resolutionAdvection time step (s)High resolution without fixerTL1279, L137600High resolution with proportional fixerTL1279, L137600High resolution with Bermejo–Conde fixerTL1279, L137600Low resolution without fixerTL255, L602700Low resolution with proportional fixerTL255, L602700Low resolution with Bermejo–Conde fixerTL255, L602700
List of the TCCON stations used in this study and ordered by latitude from north to south.
SiteLatLongReferenceEureka80.05-86.42Sodankylä67.3726.63Karlsruhe49.108.44Garmisch47.4811.06Park Falls45.94-90.27Rikubetsu43.46-143.77Lamont36.60-97.49Izaña28.30-16.48Ascension Island-7.92-14.33Darwin-12.43130.89Wollongong-34.41150.88Lauder 125HR-45.05169.68Global proportional mass fixer
The proportional mass fixer only requires the computation of the total tracer
mass before and after the SL advection step. The mixing ratio of every single
grid point is then multiplied by the same scaling factor, i.e.
ϕχjk=αϕχ*jk,α=M(ϕχ0,p0)M(ϕχ*,p*),
where (ϕχ0,p0) and (ϕχ*,p*) are the
tracer mixing ratio and the pressure field before and after the SL advection
step respectively. Long-lived tracers also require the correction of the
pressure field to ensure global mass conservation of air before computing the
scaling factor α, as already discussed at the beginning of
Sect. . The advantages of this fixer is that it is
computationally cheap, it is easy to implement, it preserves positive
definiteness, and for tracers such as CO2 and CH4 it produces
very small increments. The disadvantage is that the mass of every grid point
is adjusted by the same factor implying that regions with large transport and
mass conservation error are corrected by an equal proportion with regions
where these errors are small; therefore, the solution deteriorates there.
This scheme is used by the ACCESS and HadGEM-2
Earth system climate models.
Bermejo–Conde mass fixer
A 3-D version of the mass fixer has been implemented
in the IFS that provides an effective
alternative to the proportional global mass fixer for the simulation of
long-lived greenhouse gases. This scheme preserves the monotonicity of an
advected field (provided the original field is also monotone) and overall the
increments it computes are small. A weighted approach is used where a
different weighting factor is applied when correcting the mass mixing ratios
of different grid points. For grid points in regions where the field is
smooth the weights are very small and the correction is negligible. However, for
grid points in regions with large gradients the weight and therefore the
computed increments are larger. This is the major advantage of this method,
which is well suited for simulating the transport of long-lived gases such as
CO2 and CH4. These species are spread everywhere on the
globe,
being fairly uniform in some geographical regions (e.g. Antarctica), while
they have considerable gradients in other regions (e.g. Africa, South
America). Furthermore, the mass conserving field the scheme computes has
minimum distance from the original advected non-conserving field as it is the
solution to a minimisation problem which ensures that the increments are
overall small.
Using the notation of the previous section and ignoring for simplicity the
subscript χ, the correction the Bermejo–Conde scheme introduces to
the grid-point mixing ratio in IFS can be written as
ϕjk=ϕjk*-λwjk,λ=δM∑j=1NAj∑k=1KwjkΔpjk*g,
where δM=M(ϕχ*,p*)-M(ϕχ0,p0)
is the small global mass error. In this case, we have chosen
wjk=max0,sgn(δM)sgnϕjk*-ϕjkLϕjk*-ϕjkLβpjkpj0,
which depends on the difference between the cubic interpolated field ϕ*
and the linear one ϕL as described in .
It was argued there that an appropriate setting for the parameter β
would be 1. This conclusion was based on testing done with moist and fast
chemically active tracers which differ considerably from long-lived tracers.
Repeating these tests on CO2 and CH4, we found that using
β=2 is working more effectively. That is, the weights wjk become even
smaller in smooth regions and larger in regions with mass gradients. As this
is an even number, sgnϕjk*-ϕjkL needs to be
considered in Eq. () to allow preservation of monotonicity and
positive definiteness. Moreover, to avoid erroneously large corrections in
the stratosphere, the weight wjk is scaled by a factor of
pjkpj0 that reflects the density variation from the surface
to the top of the atmosphere. Since IFS uses a pressure-based vertical
coordinate, a good option is the ratio of the pressure at grid point jk
(pjk) to the surface pressure below this grid point (pj0).
Experiments
Several CO2 and CH4 simulations using the IFS have been
performed to test the influence of the global tracer mass fixers on their
inter-hemispheric gradient. The global proportional fixer has been used for
the low-resolution simulations and shown to provide satisfactory results in
terms of gradients in the CO2 simulation
and CH4 in the Transcom model
intercomparison studies . However,
it is not clear whether this is still the case for the high-resolution
simulations. For this reason, the global proportional fixer is compared with
the fixer using two different resolutions. One is a low
resolution corresponding to approximately 80 km in the horizontal with
60 model levels, i.e. the same as the one used by the ECMWF ERA-Interim
re-analysis and similar to that used in climate simulations
e.g.. The other resolution is approximately
16 km in the horizontal and 137 model levels, i.e. following the operational
NWP resolution also used in the operational CO2 and CH4 CAMS
forecasts. The model time steps depend on the model resolution, corresponding
to 10 and 45 min for high and low resolutions respectively. A list of all
the experiments can be found in Table .
Instantaneous
global mean mass conservation error for CO2 (ppm) and CH4 (ppb) from 1 to 31 March 2013. Low- and high-resolution experiments are depicted by red and blue lines respectively.
The simulations are performed using the cyclic forecast configuration with
the IFS NWP model. This means that the meteorology is re-initialised at
00:00 UTC using the operational ECMWF NWP analysis, but the CO2 and
CH4 tracers are allowed to evolve freely, i.e. without any constraint
from observations. The transport in the IFS is based on the semi-Lagrangian
advection scheme
described in the previous section,
as well as a turbulent mixing scheme
and a convection scheme .
The CH4 fluxes and chemical sink in the simulations are based on
prescribed climatologies and inventories as used by the operational CAMS
CH4 analysis and forecast see following
the prior fluxes and chemical sink of flux
inversion system, except for the fire emissions from the GFAS dataset
. The surface fluxes of CO2 are also the same
as those used in the operational CO2 analysis and forecast seefor a
detailed description. They are all prescribed from
inventories and climatologies, except for the land biogenic CO2
fluxes which are modelled online by the CTESSEL Carbon module
. A flux adjustment scheme has been implemented to
correct for biases in the NEE budget with respect to a climatology of
optimised fluxes from seefor further
details. The fluxes for the high and low
resolution are based on the same inventories and model. The global budget for
the prescribed fluxes is the same, but their resolution is different. Because
of that the gradients are sharper in the high resolution as the emission
hotspots are characterised by stronger fluxes with the same mass distributed
over a smaller area. For the modelled fluxes, the climate drivers such as
radiation, soil moisture and temperature might vary with the resolution, and
therefore the fluxes will not necessarily be the same. This only affects
CO2 as CH4 only has prescribed fluxes.
The CO2 and CH4 simulations have been performed from 1
March 2013 to 30 April 2014. The aim is to test the annual accumulation of
the error associated with mass conservation and the impact of the implemented
mass fixer. In order to focus on the accumulated impact, instead of the mean
impact, the evaluation of the simulations is done for the last month, and not
the whole period. The last month from 7 March to 10 April was used to compare
with the observations from the Polarstern cruise
providing a north–south transect across the Atlantic of total column-averaged
CO2 and CH4, together with observations from the Total Carbon
Column Observing Network (TCCON) . A
description of the observations used to assess the experiments is given in
the next section.
Cumulative global mean mass conservation error for CO2 (ppm)
and CH4 (ppb) from 1 to 31 March 2013. Low- and high-resolution experiments are depicted by red and blue lines respectively.
Mean XCO2 (ppm) from 7 March to 10 April 2014 for the high-resolution (left panels) and low-resolution (right panels) simulations.
The effect of the different mass fixers is shown in the different rows. Details of the simulations can be found in Table .
The pink and black triangles mark the location of the reference observations from TCCON and Polarstern cruise respectively.
See Table for a list of the TCCON site coordinates.
Observations
The ship-based Polarstern dataset provides an
excellent opportunity to assess the inter-hemispheric gradient, as it samples
mainly oceanic well-mixed background air. The research vessel Polarstern
took off from Cape Town (34∘ S, 18∘ E), South Africa, on
5 March 2014, and entered port at Bremerhaven (54∘ N,
19∘ E), Germany, on 14 April 2014. During the cruise, an EM27/SUN
near-infrared spectrometer was deployed onboard Polarstern. It collected
direct-sun absorption spectra allowing the retrieval of XCO2 and
XCH4 with high precision and accuracy
as detailed for the
Polarstern campaign by . Post-campaign deployment
of the EM27/SUN side by side the TCCON spectrometer at Karlsruhe, Germany,
allowed the calibration of XCO2 and XCH4 to the World
Meteorological Organization (WMO) standard.
estimated the precision of the retrieved mole fractions to be to better than
0.2 ppm and 0.7 ppb for XCO2 and XCH4,
respectively. This remote sensing technique samples the entire total column
abundance and it is less dependent on localised sources in comparison to
in situ measurements.
All observations from 40∘ S to 40∘ N across the eastern
Atlantic Ocean were used. Information on the prior and averaging kernel was
also used in order to be able to compare the observations with the model
following .
While Polarstern data provide a clear sampling of the meridional profile of
background air representative of the large-scale inter-hemispheric gradient,
they are not part of an operational network. For this reason, the evaluation of
the inter-hemispheric gradient is corroborated using the TCCON observations.
Observations from the TCCON are regularly used
as a reference of total column CO2 and CH4 to calibrate and
evaluate CO2 and CH4 products by the satellite community
e.g. and modelling community
e.g..
In this study, we used the version GGG2014 of the TCCON data
(, tccon.ornl.gov).
TCCON sites used to assess the inter-hemispheric gradient are listed in
Table .
Mean XCH4 (ppb) from 7 March to 10 April 2014 for the high-resolution (left panels) and low-resolution (right panels) simulations.
The effect of the different mass fixers is shown in the different rows. Details of the simulations can be found in Table . The pink and black
triangles mark the location of the reference observations from TCCON and Polarstern cruise respectively.
See Table for a list of the TCCON site coordinates.
Difference in mean XCO2 (ppm) between (a, b) the simulations using the proportional mass fixer and the simulation without mass fixer at high and low
resolution respectively; (c, d) the simulation with Bermejo–Conde and the simulation without mass fixer at high and low resolutions respectively.
The period covered and the marking of the observation sites are the same as in Fig. . See Table for a list of the TCCON site coordinates.
Difference in mean XCH4 (ppb) between (a, b) the simulations using the proportional mass fixer and the simulation without mass
fixer at high and low resolution respectively; (c, d) the simulation with Bermejo–Conde and the simulation without mass fixer at high
and low resolutions respectively. The period covered and the marking of the observation sites are the same as in Fig. . See Table for a list of the TCCON site coordinates.
Results
The impact of the mass fixers is assessed with global budget diagnostics
(Sect. ), monthly mean total column maps
(Sect. ) and comparisons with observations of the
inter-hemispheric gradient (Sect. ).
For the global mass diagnostics, the mass of the CO2 and CH4
tracers is computed using Eq. (). In the results that follow, the
global error in tracer mass conservation during the advection to be corrected
is computed as molar fraction in part per million following
DM=M(ϕ*,p*)-M(ϕo,po)M(po)mairmCO2×106,
where p* is the pressure field after advection, which has been corrected with a mass fixer to conserve global atmospheric mass (i.e. M(po)=M(p*)).
Global mass conservation error
The instantaneous global mean mass conservation error per time step computed
for the low- and high-resolution simulations using Eq. () is mostly
positive (Fig. ). The value oscillates around 1.2×10-4 ppm for CO2 and around 2.6×10-3 ppb for
CH4 in the low-resolution simulation. The error in the high-resolution simulation is only slightly lower for CO2 (0.8×10-4 ppm) and much lower for CH4 (0.6×10-3 ppb) than in the low-resolution simulation. The oscillations
around the mean value are also smaller.
(a) Map showing the daily mean sampling location of Polarstern cruise.
(b, c) Comparisons of latitudinal distribution of XCO2 and
XCH4 as derived from monthly mean (7 March to 10 April) Polarstern
observations (black) and simulations using different mass fixers at different
resolutions: red and orange lines denote without mass fixer at low and high resolutions respectively; blue and
cyan lines
with the proportional mass fixer at low and high resolutions respectively; and green and light
green with the Bermejo–Conde fixer and low and high resolutions respectively.
See Table for a more detailed description of the
experiments.
Comparisons of latitudinal distribution of (a)XCO2 and (b)XCH4 as derived from monthly mean (7 March to 10 April)
TCCON sites (black, see Table ) and simulations using
different mass fixers at different resolutions: red and orange without mass fixer
at low and high resolutions respectively; blue and cyan with the proportional mass fixer at
low and high resolutions respectively; and green and light green with the Bermejo–Conde fixer
and low and high resolutions respectively. See Table for a more
detailed description of the experiments.
Although the instantaneous global mass conservation error per time step is
small relative to the mean value of CO2 and CH4 (400 ppm and
1800 ppb respectively), the error is accumulated during the simulation. If
the simulation is not re-initialised but cycled from one day to the next as
in cyclic forecasts or climate runs, then
this error will grow with time as shown in Fig. . The
error growth rate is faster in the high resolution than in the low-resolution
simulation by a factor of 3.2 for CO2 and 1.1 for CH4,
despite the smaller instantaneous errors in the high-resolution simulation.
This is because the time step is a factor of 4.5 smaller than in the low-resolution simulation. Therefore, the advection scheme
is called more frequently, leading to a faster error accumulation.
After 1 month, the conservation error reaches the value of 0.37 ppm for
CO2 and 2.79 ppb for CH4 in the high-resolution simulation.
This is equivalent to an annual growth of 4.4 ppm year-1 and
33.0 ppb year-1 for CO2 and CH4 respectively. These
error values are larger than the current observed growth of CO2from 1 to 3 ppm year-1; see and
CH4from 0.6 to 16 ppb year-1; see.
Impact of mass fixers on total column CO2 and CH4 spatial distribution
The maps of mean XCO2 and XCH4 from 7 March to 10 April 2014
during the period of the Polarstern cruise (Figs. and
) highlight the dominant inter-hemispheric gradient. After
approximately 1 year of simulation without the mass fixer, the mean values
of XCO2 and XCH4 are much higher everywhere, but
particularly in the source regions in the Northern Hemisphere (e.g. over Southeast Asia).
The high-resolution simulation in Figs. a and
a displays an enhanced increase with respect to the low-resolution simulation (Figs. b and b).
For example, in Southeast Asia the XCO2 enhancement is around 4 ppm
and the XCH4 enhancement is around 40 ppb.
XCO2 inter-hemispheric gradient (IHG) error (MODEL - OBS)
statistics for simulations with different resolution and different mass
fixers with respect to observations from the Polarstern cruise.
DataIHGIHG errorOverall biasInter-station bias(ppm)(ppm)(ppm) (%)(ppm) (%)OBS4.29Low resolution without fixer7.813.522.70 (0.68)1.54 (0.39)Low resolution with proportional fixer7.703.420.82 (0.21)1.50 (0.38)Low resolution with Bermejo–Conde7.112.820.62 (0.16)1.30 (0.33)High resolution without fixer10.546.257.86 (1.98)2.54 (0.64)High resolution with proportional fixer10.175.891.36 (0.34)2.40 (0.60)High resolution with Bermejo–Conde7.973.690.69 (0.17)1.61 (0.40)Spread of low-resolution simulations0.700.702.01 (0.51)0.24 (0.06)Spread of high-resolution simulations2.572.567.17 (1.81)0.93 (0.24)Spread of low-resolution Bermejo–Conde and proportional0.590.600.20 (0.04)0.20 (0.05)Spread of high-resolution Bermejo–Conde and proportional2.202.200.67 (0.17)0.79 (0.20)
XCO2 inter-hemispheric gradient (IHG) error (MODEL - OBS) statistics for simulations with different resolution and different mass fixers with
respect to observations from TCCON.
DataIHGIHG errorOverall biasInter-station bias(ppm)(ppm)(ppm) (%)(ppm) (%)OBS5.76Low resolution without fixer7.481.712.71 (0.68)1.21 (0.30)Low resolution with proportional fixer7.451.680.83 (0.21)1.20 (0.30)Low resolution with Bermejo–Conde6.931.160.69 (0.17)1.02 (0.26)High resolution without fixer10.144.387.94 (1.99)2.16 (0.54)High resolution with proportional fixer10.044.281.44 (0.36)2.13 (0.54)High resolution with Bermejo–Conde8.102.340.88 (0.22)1.45 (0.37)Spread of low-resolution simulations0.550.552.02 (0.51)0.19 (0.05)Spread of high-resolution simulations2.042.047.06 (1.77)0.71 (0.17)Spread of low-resolution Bermejo–Conde and proportional0.520.520.14 (0.04)0.18 (0.05)Spread of high-resolution Bermejo–Conde and proportional1.941.940.56 (0.14)0.68 (0.17)
XCH4 inter-hemispheric gradient (IHG) error (MODEL - OBS) statistics for simulations with different resolution and different mass fixers with
respect to observations from the Polarstern cruise.
DataIHGIHG errorOverall biasInter-station bias(ppb)(ppb)(ppb) (%)(ppb) (%)OBS53.81Low resolution without fixer73.4219.6141.09 (2.28)9.88 (0.55)Low resolution with proportional fixer70.6516.841.74 (0.10)8.91 (0.50)Low resolution with Bermejo–Conde54.290.486.58 (0.37)4.84 (0.27)High resolution without fixer92.0038.1955.83 (3.10)16.84 (0.94)High resolution with proportional fixer88.1934.386.05 (0.34)15.36 (0.85)High resolution with Bermejo–Conde55.711.901.82 (0.10)4.64 (0.26)Spread of low-resolution simulations19.1319.1339.35 (2.18)5.05 (0.28)Spread of high-resolution simulations36.2936.2954.01 (3.00)12.20 (0.68)Spread of low-resolution Bermejo–Conde and proportional16.3616.362.01 (0.11)4.07 (0.23)Spread of high-resolution Bermejo–Conde and proportional33.9032.484.23 (0.24)10.72 (0.59)
XCH4 inter-hemispheric gradient (IHG) error (MODEL - OBS) statistics for simulations with different resolution and different mass fixers with
respect to observations from TCCON.
DataIHGIHG errorOverall biasInter-station bias(ppb)(ppb)(ppb) (%)(ppb) (%)OBS52.64Low resolution without fixer77.5424.9052.28 (2.92)14.17 (0.79)Low resolution with proportional fixer76.0623.4214.77 (0.83)13.76 (0.77)Low resolution with Bermejo–Conde60.968.3211.47 (0.64)9.02 (0.50)High resolution without fixer91.6238.9866.68 (3.72)18.76 (1.05)High resolution with proportional fixer89.6437.0016.70 (0.93)18.16 (1.01)High resolution with Bermejo–Conde59.787.149.90 (0.55)7.62 (0.43)Spread of low-resolution simulations16.5816.5840.81 (2.28)5.15 (0.29)Spread of high-resolution simulations31.8431.8456.78 (3.17)11.14 (0.62)Spread of low-resolution Bermejo–Conde and proportional15.1015.103.30 (1.19)4.74 (0.27)Spread of high-resolution Bermejo–Conde and proportional29.8629.866.80 (0.38)10.54 (0.58)
Error (%) of modelled latitudinal monthly mean (7 March to 10 April) distribution computed as (MODEL - OBS)/OBS
using different tracer mass fixers and different resolutions for
(a–c)XCO2 and (d–f)XCH4 with respect to
the observed distribution from Polarstern. Dark and light colours correspond to
the simulations at low and high resolution respectively.
Error (%) of modelled latitudinal monthly mean (7 March to 10 April) distribution computed as (MODEL - OBS)/OBS
using different tracer mass fixers and different resolutions for
(a–c)XCO2 and (d–f)XCH4 with respect to
the observed distribution from TCCON. Dark and light colours correspond to the
simulations at low and high resolution respectively.
Schematic illustrating the impact of the (a) proportional and (b) Bermejo–Conde mass fixers on the inter-hemispheric
gradient of XCO2 and XCH4. Note that the area between the dash line and thin solid line depicting the global correction of tracer mass should be the same for the two mass fixers.
Both proportional and Bermejo–Conde
mass fixers reduce the mean XCO2 and XCH4 values everywhere,
as intended. However, the proportional mass fixer leads to slightly different
spatial distribution for the high- and low-resolution simulations
(Figs. c, d and c, d), whereas the two
spatial distributions obtained by using Bermejo–Conde remain closer to one
another for the two different resolutions (Figs. e, f and
e, f). Some differences in the regions of sources and sinks
are expected since the surface fluxes are also affected by the resolution
change. For example, emission hotspots can be distributed over a smaller area and
become more intense. However, this is not the case over Antarctica and the
Southern Ocean, where surface fluxes are very weak. The impact of the
resolution south of 40∘ S is indeed striking, particularly for the
proportional mass fixer (Figs. c, d and
c, d). Over that region the mean XCO2 and
XCH4 are 2 to 4 ppm and 20 to 40 ppb lower in the proportional mass
fixer simulation at high resolution than all other simulations. This
large-scale mean negative difference cannot be explained by differences in
fluxes or transport. Thus, it has to be linked to the mass conservation
error and the effect of the proportional mass fixer, enhanced by the action
of the mass fixer at high resolution (see Sect. ).
The effect of the mass fixers can be seen more clearly in
Figs. and by computing the
difference between the fields resulting from the different mass fixers with
the fields from the simulation without any mass fixer. The proportional mass
fixer removes mass quite uniformly for both the high- and low-resolution
simulations, albeit with higher magnitude for the high-resolution case
(Figs. a, b and a, b). For
example, the decrease in XCO2 is around 2 ppm in the low-resolution
simulation, and around 10 ppm in the high-resolution simulation. The
XCH4 decrease is not as uniform as in XCO2, being larger in
the Northern Hemisphere mid-latitudes by approximately 10 ppb at high
resolution. On the other hand, the Bermejo–Conde mass fixer removes even
more mass in the Northern Hemisphere than in the Southern Hemisphere,
particulary at high resolution (see Figs. c, d and
c, d). This is a desirable effect, since the
conservation error is expected to be larger closer to the sources and/or sinks in
the Northern Hemisphere.
Evaluation of inter-hemispheric gradient with observations
Comparing the simulations to the observed north–south transect in
March–April 2014 we see that all the model simulations can represent the sign
of the XCO2 and XCH4 gradient with larger values in the
Northern Hemisphere and lower in the Southern Hemisphere (see
Figs. and ).
The errors with respect to both TCCON and Polarstern-observed gradients are
shown in Figs. and .
The gradient of both XCO2 and XCH4 is steepest at high
resolution without the mass fixer, compared to the lower-resolution
simulation and also to other simulations with the mass fixer. This corroborates
the detrimental enhancement of XCO2 and XCH4 – particularly in
the Northern Hemisphere – associated with the accumulation of mass
conservation errors. The proportional mass fixer also results in a gradient
which is too steep, particularly at high resolution (see light blue line in
Figs. and ). The simulation with
the Bermejo–Conde fixer has the gradient closest to the observed profiles.
It also presents the best consistency (i.e. smallest difference) between
high-
and low-resolution simulations.
The inter-hemispheric gradient can be quantified as the difference between
the tracer in the Northern Hemisphere and Southern Hemisphere. Here we take
between 20 and 50∘ N and between 20 and 40∘ S for the two
hemispheres due to the availability of observations. For XCO2 the
observed difference is 4.29 and 5.76 ppm using the Polarstern and the TCCON
datasets respectively. For XCH4 the gradient is 53.81 and 52.64 ppb
for the same datasets respectively. The gradient for the different
experiments is shown in Tables to
. All the low-resolution simulations have a similar
gradient of XCO2 of approximately 7 ppm with a range of 0.7 ppm
(Polarstern) and 0.6 ppm (TCCON). That is, the range of inter-hemispheric
gradients at the low resolution is around 10 % of its value, whereas the
high-resolution simulations have a larger range of 2 ppm corresponding to a
30 % spread. This highlights the distorting effect of the mass conservation
error on the inter-hemispheric gradient. For XCH4 the effect is
similar, albeit even more pronounced than for XCO2 in the low-resolution simulations, where the range of the inter-hemispheric gradient
values is around 18 ppb (i.e. 34 % of its value). At high resolution the
XCH4 range is around 34 ppb (i.e. 63 %).
When looking at the impact of each fixer, we see that the simulation with the
proportional mass fixer has the same error in inter-hemispheric gradient as
the simulation without mass fixer (i.e. 4.3 to 5.9 ppm at high resolution
and 1.6 to 3.4 ppm at low resolution, comprising 75 to 140 % of the error
at high resolution and 32 to 79 % at low resolution). It is clear that the
error grows with high resolution. This goes against all expectations as the
objective of high-resolution simulations is to achieve a better accuracy. On
the other hand, the Bermejo–Conde fixer is able to keep a closer gradient
between the low- and high-resolution simulations (within 1 ppm and 2 ppb for
XCO2 and XCH4). The resulting error with respect to both
Polarstern and TCCON is nearly half the inter-hemispheric error of the
proportional mass fixer.
These results are consistent with the station-to-station bias, which is
computed as the standard deviation of the biases from the individual stations
or cruise observations. The results are very similar when either there is no
mass fixer or the proportional fixer mass is used. For XCO2 the
inter-station bias is 2 and 1.2 ppm at high and low resolutions
respectively. However, for XCH4 the inter-station bias ranges from 14 to
19 ppb and from 9 to 14 ppb at high and low resolutions respectively. The
Bermejo–Conde is again showing an improvement with similar values for the
high- and low-resolution simulations of around 1.4 ppm for XCO2 and
around 4.8 ppb for XCH4. These values are in line with the
variability of the bias in space and time obtained from satellite retrievals
of GOSAT .
The effect of both proportional and Bermejo–Conde mass fixers on the bias
with respect to observations is similar. They both manage to reduce the bias
from around 2 % to less than 0.4 % for XCO2 and from around 4 %
to less than 1 % for XCH4. It is worth noting that even for the
bias, the Bermejo–Conde is able to have a reduction of the bias error of
at least 0.1 % with respect to the proportional mass fixer, leading to an
overall bias of 0.2 % (∼ 0.7 ppm).
It is also remarkable that the resulting errors associated with the
inter-hemispheric gradient are the same when using TCCON and Polarstern
observations, despite being at different sampling sites (i.e. along different
longitudes). The uniformity of the results throughout the globe means that
the main error source is global. This is consistent with global error source
of the mass fixer. Therefore, it strengthens the suggestion that the
observations used here are able to detect the effects of the mass fixer more
than the other effects associated with localised error sources from local
fluxes and/or regional transport.
Conclusions
Atmospheric transport schemes used in models to monitor and/or predict climate
change and atmospheric composition are required to conserve the global mass
of atmospheric tracers. Thus, the use of numerical methods that do not
inherently conserve mass, such as the widely used semi-Lagrangian advection
scheme, entail the application of mass fixers to ensure the preservation of
the global mass. This is particularly important for long-lived greenhouse
gases for which the interesting signals to monitor (e.g. annual growth rates
and large-scale spatial gradients) are weak compared to their background
values. This paper explores the impact of two global mass fixers on the
inter-hemispheric gradient of total column-averaged CO2 and
CH4 using observations from the Polarstern cruise and the TCCON. The widely used proportional fixer is compared to the Bermejo–Conde fixer, presenting a feasible alternative in the context of operational
atmospheric transport models.
Two different resolutions are also compared, the first one is a typical
climate resolution of 80 km and 60 model levels and the second one is the
current resolution used in NWP at 16 km in the horizontal and 137 model
levels. Results clearly show that errors accumulate much faster for the high-resolution simulations and after 1 year the mass conservation error exceeds
by far the observed annual growth rate of CO2 and CH4. The
mass conservation errors of XCO2 and XCH4 grow faster in the
Northern Hemisphere than in the Southern Hemisphere, causing a steepening of
the inter-hemispheric gradient. The proportional mass fixer applies a uniform
correction globally because it only depends on the background value which is
uniformly high. Thus, the proportional fixer is efficient at removing the
global bias, but it cannot correct for the steepening of the
inter-hemispheric gradient. This is detected as an artificial reduction of
XCO2 and XCH4 in the Southern Hemisphere and a resulting
excess in the Northern Hemisphere when comparing with observations as
depicted in Fig. . On the other hand, the
alternative Bermejo–Conde fixer enhances the mass correction in the
regions where gradients are steeper. CO2 and CH4 gradients
are steeper where their surface fluxes are stronger, i.e. in the Northern
Hemisphere. The Bermejo–Conde mass fixer correction is therefore
latitudinally dependent and it is able to correct the inter-hemispheric
gradient, bringing the low- and high-resolution simulations closer to each
other and closer to the observations.
In summary, the tests performed using the IFS show that although the
proportional mass fixer is suitable at low resolutions currently used in NWP
re-analysis and climate simulations, it is not suitable for NWP resolutions
at 16 km and 137 vertical levels. An alternative global mass fixer based on
Bermejo–Conde has been shown to work reasonably well when compared to
observations at both low and high resolutions without too much additional
complexity or cost.
Code and data availability
This particular study has been based on the IFS model cycle 41R2.
The C-IFS source code is integrated into ECWMF's
IFS code, which is only available subject to a licence
agreement with ECMWF. ECMWF member-state weather
services and their approved partners will get access
granted. The IFS code without modules for assimilation
and chemistry can be obtained for educational and academic
purposes as part of the openIFS release (https://software.ecmwf.int/wiki/display/OIFS/OpenIFS+Home).
A detailed documentation of the IFS code is available from
https://software.ecmwf.int/wiki/display/IFS/CY40R1+Official+IFS+Documentation.
The output from C-IFS can be requested via
http://copernicus-support.ecmwf.int. The Polarstern data is available
in the Supplement of at
10.5194/amt-8-5023-2015-supplement. The TCCON data (version GGG2014 )
is available from tccon.ornl.gov.
Acknowledgements
This study has been funded by the European Commission under
Monitoring of Atmospheric Composition and Climate project and
the Copernicus Atmosphere Monitoring Service.
F. Klappenbach and A. Butz acknowledge support by Frank Hase, KIT, for instrument
development and data reduction, by the Emmy Noether
Programme of the Deutsche Forschungsgemeinschaft (DFG) through
grant BU2599/1-1 (RemoteC), and by Alfred Wegener Institute (AWI),
Helmholtz Centre for Polar and Marine Research, for operating RV
Polarstern and granting access to its infrastructures.
TCCON data were obtained from the TCCON Data Archive, hosted by the Carbon
Dioxide Information Analysis Center (CDIAC) –
tccon.onrl.gov. The authors would like to
acknowledge the PIs of the different TCCON stations used in this study:
Kimberly Strong (Eureka, Canada) Rigel Kivi (Sodankylä, Finland),
Frank Hase (Karlsruhe, Germany), Ralf Sussmann (Garmisch, Germany),
Paul Wennberg (Park Falls, Lamont, USA), Matthias Schneider (Izaña, Spain),
Dietrich Feist (Ascension Island), David Griffith (Darwin, Wollongong,
Australia), Dave Pollard and Vanessa Sherlock (Lauder, New Zealand). The
operation at the Rikubetsu TCCON site is supported in part by the budget from
the GOSAT data validation project funded by the Ministry of Environment,
Japan.
The authors are grateful to Sebastien Massart and Johannes Flemming for useful discussions and comments during the completion of this work.
Edited by: S. Remy
Reviewed by: two anonymous referees
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