GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus PublicationsGöttingen, Germany10.5194/gmd-9-1683-2016Sensitivity of chemistry-transport model simulations to the duration of
chemical and transport operators: a case study with GEOS-Chem v10-01PhilipSajeevsj207331@dal.caMartinRandall V.https://orcid.org/0000-0003-2632-8402KellerChristoph A.Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, CanadaHarvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, USASchool of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, USAnow at: Universities Space Research Association/GESTAR, NASA GMAO Code 610.1, Greenbelt, Maryland, USASajeev Philip (sj207331@dal.ca)3May2016951683169515September20153November201521April201622April2016This 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/9/1683/2016/gmd-9-1683-2016.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/9/1683/2016/gmd-9-1683-2016.pdf
Chemistry-transport models involve considerable computational expense. Fine
temporal resolution offers accuracy at the expense of computation time.
Assessment is needed of the sensitivity of simulation accuracy to the
duration of chemical and transport operators. We conduct a series of
simulations with the GEOS-Chem chemistry-transport model at different
temporal and spatial resolutions to examine the sensitivity of simulated
atmospheric composition to operator duration. Subsequently, we compare the
species simulated with operator durations from 10 to 60 min as typically
used by global chemistry-transport models, and identify the operator
durations that optimize both computational expense and simulation accuracy.
We find that longer continuous transport operator duration increases
concentrations of emitted species such as nitrogen oxides and carbon monoxide
since a more homogeneous distribution reduces loss through chemical reactions
and dry deposition. The increased concentrations of ozone precursors increase
ozone production with longer transport operator duration. Longer chemical
operator duration decreases sulfate and ammonium but increases nitrate due to
feedbacks with in-cloud sulfur dioxide oxidation and aerosol thermodynamics.
The simulation duration decreases by up to a factor of 5 from fine (5 min)
to coarse (60 min) operator duration. We assess the change in simulation
accuracy with resolution by comparing the root mean square difference in
ground-level concentrations of nitrogen oxides, secondary inorganic aerosols,
ozone and carbon monoxide with a finer temporal or spatial resolution taken
as “truth”. Relative simulation error for these species increases by more
than a factor of 5 from the shortest (5 min) to longest (60 min) operator
duration. Chemical operator duration twice that of the transport operator
duration offers more simulation accuracy per unit computation. However, the
relative simulation error from coarser spatial resolution generally exceeds
that from longer operator duration; e.g., degrading from
2∘× 2.5∘ to 4∘× 5∘
increases error by an order of magnitude. We recommend prioritizing fine
spatial resolution before considering different operator durations in offline
chemistry-transport models. We encourage chemistry-transport model users to
specify in publications the durations of operators due to their effects on
simulation accuracy.
Introduction
Global and regional chemistry-transport models (CTMs) have a wide range of
applications in studies of climate, air quality, and biogeochemical cycling.
The last few decades have witnessed rapid development of modeling
sophistication to tackle these issues, but that development is associated
with increasing computational expense. Typically, Eulerian models divide the
atmosphere into numerous (104–108) grid boxes and solve the mass
continuity equation to simulate atmospheric composition. Numerical solution
of the mass continuity equation involves separating the different chemical
and transport processes (or operators) through operator splitting. The
concentrations of simulated species are sensitive to the duration of
operators used in the CTM. Attention is needed to understand how operator
duration affects model performance.
Numerous studies have examined the sensitivity of simulations to grid
resolution for ozone (Jang et al., 1995; Esler et al., 2004; Ito et al.,
2009; Yu et al., 2016), ozone production efficiency (Liang and Jacobson,
2000), and ozone sensitivity to precursor emissions (Cohan et al., 2006;
Henderson et al., 2010). Simulation error increases proportional to the size
of the horizontal grid (Wild and Prather, 2006; Prather et al., 2008). Biases
can be reduced by simulating sub-grid-scale processes such as emission plumes
from point sources (Sillman et al., 1990; Valin et al., 2011), aircraft
exhaust (Kraabøl et al., 2002), ship exhaust (Vinken et al., 2011),
mineral dust emissions (Ridley et al., 2013), and lightning (Cooper et al.,
2014). The spatial and temporal resolution of the meteorological fields used
in CTMs can also influence model processes (Bian et al., 2009). The
spatiotemporal variation of carbon monoxide is better represented with finer
grid resolution (Wang et al., 2004; Chen et al., 2009; Yan et al., 2014).
Moreover, fine horizontal resolution is important for air quality exposure
assessment and health impact studies (Punger and West, 2013; Fountoukis et
al., 2013; Thompson et al., 2014; Li et al., 2015). Fine vertical resolution
can better represent the effects of convection (Rind et al., 2007; Arteta et
al., 2009). Simulations are also sensitive to operator durations (Mallet et
al., 2007; Santillana et al., 2016), however, few studies have examined this
sensitivity.
CTMs solve the continuity
equation for tens to hundreds of chemical species, each with number density
n, for individual grid boxes defined in the Eulerian model.
∂n∂t=-∇×nU+P-L∂n/∂t represents the local temporal evolution of n.
-∇×nUrepresents the transport flux divergence term,
where U is the wind velocity vector. P and L are the local
production and loss terms respectively. Typically, the above equation is
discretized in space, and the continuity equation is simulated as a system of
coupled nonlinear partial differential equations with chemical and transport
operators. These chemical and transport operators are usually simulated
sequentially through operator splitting to increase computational efficiency
(Hundsdorfer and Verwer, 2003). The transport operator involves solving the
3-D advection equation using efficient numerical schemes (Prather, 1986; Lin
and Rood, 1996). Boundary layer mixing, convection, emission and deposition
are often simulated as individual operators. The chemical operator
representing the temporal evolution of local sources and sinks involves
numerically solving a system of coupled ordinary differential equations using
efficient solvers (Jacobson and Turco, 1994; Damian et al., 2002). The
integration time step in a differential equation solver is important for
efficient and accurate solution (Jacobson and Turco, 1994). Moreover, the
model accuracy is affected by the duration of chemical and transport
operators (Mallet and Sportisse, 2006; Mallet et al., 2007), and the order in
which these operators are applied (Sportisse, 2000; Santillana et al., 2016).
The operator splitting method requires the coupling between individual
operators to be negligible over the operator duration. However, reducing
operator durations increases computational expense. Attention is needed to
this tradeoff.
We examine the sensitivity of a CTM to operator duration by conducting a
series of simulations at different horizontal resolutions and operator
durations. We then identify the optimal operator duration from the range of
operator durations from 10 to 60 min usually used by global CTMs (e.g.,
Horowitz et al., 2003; Huijnen et al., 2010). Section 2 describes the
sensitivity simulations, the method to quantify the simulation error, as
well as the method to identify the simulation operator durations that best
account for both computational expense and simulation accuracy. Comparison
of the sensitivity simulations, description of resolution-dependent errors,
and the identification of appropriate chemical and transport operator
durations are examined in Sect. 3.
Materials and methodsGEOS-Chem simulations
We conduct a series of sensitivity simulations with the GEOS-Chem CTM
(version 10-01; www.geos-chem.org) at different horizontal resolutions
and operator durations to examine the individual sensitivities to chemical
and transport operator durations. The GEOS-Chem model (Bey et al., 2001) is
used by about 100 research groups worldwide to simulate the oxidant–aerosol
system. GEOS-Chem has the capability to be driven with several generations of
assimilated meteorological data from the Goddard Earth Observing System
(GEOS) at the NASA Global Modeling Assimilation Office (GMAO). For
computational expedience, GEOS-Chem global simulations are often conducted
using horizontal resolutions of either 4∘× 5∘ or
2∘× 2.5∘ degraded from the native resolution of
GEOS meteorology. GEOS-Chem also has the capability for nested regional
simulations where the global model provides dynamic boundary condition to the
finer regional grids (Wang et al., 2004; Chen et al., 2009; Zhang et al.,
2011; van Donkelaar et al., 2012). We use the GEOS-5.2.0 meteorology
available at a native horizontal resolution of
0.5∘× 0.667∘ (Rienecker et al., 2008). It includes
3 h averaged 2-D fields such as mixed layer depth, and 6 h averaged 3-D
fields such as zonal and meridional wind, and convective mass flux. The
height of the lowest level of the model is approximately 130 m above the sea
level, with 47 vertical levels.
GEOS-Chem performs species advection (A), vertical mixing (V), cloud
convection (Z) and wet deposition (W) for every transport operator duration
(T), as well as dry deposition (D), emissions (E), and chemistry (G) for
every chemical operator duration (C) in the following order,
A(T)×D(C)×E(C)×V(T)×Z(T)×G(C)×W(T)
The traditional transport operator durations are 30 min at
4∘× 5∘ resolution, 15 min at
2∘× 2.5∘ resolution, and 10 min at
0.5∘× 0.667∘ resolution. The traditional chemical
operator duration is set to either 60 min or twice the transport operator
duration based on the Strang operator splitting scheme (Strang, 1968) which
follows T×C×T×T×C×T order repetitively
with C=2×T. Transport operations are repeated twice before a
chemical operation when C=2×T. We also consider an alternate
splitting scheme, which follows T×C×T×C order,
repetitively, with C=T. Changes in operator duration from C=2×T to C=T include effects of both time truncation (T×T to T)
and operator splitting.
Advection is based on the multi-dimensional flux-form semi-Lagrangian
advection scheme (Lin and Rood, 1996; Lin et al., 1994), with an additional
pressure-fixer algorithm implemented for the conservation of species mass
(Rotman et al., 2004). The cloud convection operator couples transport by
convection (Balkanski et al., 1993; Wu et al., 2007) with gas–aerosol wet
deposition (Liu et al., 2001; Wang et al., 2011; Amos et al., 2012).
GEOS-Chem uses an internal integration time step of 5 min for convective
mixing within the cloud convection operator. The wet deposition operator
includes scavenging by large-scale precipitation through first order
operators, rainout and washout (Balkanski et al., 1993). We use a non-local
boundary layer mixing scheme for vertical transport (Holtslag and
Boville, 1993; Lin and McElroy, 2010). Emissions are processed through the
HEMCO module (Keller et al., 2014). A resistance-in-series method is used for
dry deposition of species (Wesely, 1989; Wang et al., 1998; Zhang et al.,
2001; Fisher et al., 2011).
GEOS-Chem uses a sparse matrix vectorized GEAR II chemistry solver (Jacobson
and Turco, 1994; Jacobson, 1995, 1998). The oxidant–aerosol chemistry
simulation includes organic and black carbon (Park et al., 2003), mineral
dust (Fairlie et al., 2007; Zender et al., 2003; Ginoux et al., 2001), sea
salt (Alexander et al., 2005; Jaeglé et al., 2011), and the
sulfate–nitrate–ammonium system (Park et al., 2004). The photolysis
frequency is calculated (Mao et al., 2010; Eastham et al., 2014) at the
middle of the chemical operator duration using the Fast-JX algorithm (Bian
and Prather, 2002). Simulation of gas–aerosol interactions are performed
within the chemistry operator by aerosol extinction effects on photolysis
rates (Martin et al., 2003), and heterogeneous chemistry (Jacob, 2000)
including aerosol uptake of N2O5 (Evans and Jacob, 2005) and
HO2 (Mao et al., 2013). The ISORROPIA II thermodynamic module (Fontoukis
and Nenes, 2007) performs aerosol–gas partitioning (Pye et al., 2009).
We conduct simulations for 2010 July at two horizontal resolutions of
4∘× 5∘ and 2∘× 2.5∘
globally, and 0.5∘× 0.667∘ over the North America
(140–40∘ W, 10–70∘ N) and East Asia (70–150∘ W,
11∘ S–55∘ N) nested regions. We use the
4∘× 5∘ global simulation to archive dynamic
boundary conditions every 3 h for the nested simulations. We use a 1-month
spin-up with each GEOS-Chem simulation to reduce the influence of initial
conditions.
Computing platform
We conduct all simulations on the same computing platform to compare their
computational performance. We use the Glooscap cluster of the Atlantic
Computational Excellence Network (ACENET) Consortium of Canadian Universities
(http://www.ace-net.ca/wiki/Glooscap). The operating system is
Linux 4.8. We use Intel Fortran compiler version 12. Each GEOS-Chem
simulation is submitted as a 16-thread parallelized job on a single node.
We calculate the CPU time for the month of July for each operator separately
using the Fortran-intrinsic routine, CPU_TIME. We found this
value identical to the one calculated using the Linux command “qacct –j”.
To reduce the effects of other jobs on the shared cluster, we repeat
simulations five times, while excluding data output operations to minimize
sensitivity to system input/output, and use the median to represent CPU
time. We also report the standard error over the five simulations.
CPU time for GEOS-Chem simulations with various operator durations
at three horizontal resolutions. Global simulations are at
4∘× 5∘(a) and
2∘× 2.5∘(b) resolutions.
Panel (c) contains results for the average of two nested regions
North America and East Asia at 0.5∘× 0.667∘
resolution. Colored lines represent the CPU time for simulating transport
(red) and chemical (blue) operators, and the sum of the two (green). Error
bars represent standard error over five simulations. Simulations are
represented in the abscissa as CccTtt with chemical operator duration, C=cc min, and transport operator duration, T=tt min.
Assessing the relative simulation error
We treat the simulation with the shortest operator duration as the most
accurate. This approach exploits the reduction in error associated with
coupling across operators as operator duration diminishes. Assessing
simulation error vs. operator duration through comparison with observations
is impaired by imperfect model processes, by the sparseness of measurements,
and by model–observation representativeness biases. We take as “truth” the
concentrations simulated with a chemical operator duration (C) of 10 min
and a transport operator duration (T) of 5 min (represented as C10T05).
Finer resolutions are computationally prohibitive. We define the relative
simulation error Esims for species s as the root mean
square error (RMSE) of the species concentrations simulated with the finest
resolution (“truth”) and the simulation under consideration (Sim),
normalized by the concentrations in simulation “truth”,
Esims=N∑i=1i=NTruthis-Simis2∑i=1i=NTruthis
where, i represents a particular grid box, with a total number of N grid boxes
of interest. RMSE in the numerator is chosen instead of absolute difference
to more heavily penalize extrema. Normalization with the mass of the
“true” simulation is intended to cross-compare Esims of different
species. Esims captures the variation of a species s from the
“true” simulation.
We focus on four key species relevant to atmospheric chemistry, namely
nitrogen oxides (NOx= NO + NO2), secondary inorganic
aerosols (SIA: sum of sulfate, nitrate and ammonium), ozone (O3), and
carbon monoxide (CO). These species represent a range of lifetimes from a
day (NOx) to weeks (CO). The focus on SIA is designed to devote more
attention to chemically active species than to mineral dust and sea salt. We
sample the instantaneous values of simulated ground-level concentrations of
these atmospheric species every 60 min to span the diurnal variation of
chemical environments. We focus on concentrations in July near the Earth's
surface when and where chemical and transport timescales tend to be short.
(a) Sensitivity of simulated species to the duration of
chemical and transport operators. The left column contains monthly mean
ground-level concentrations simulated with the shortest operator duration
considered (C10T05) at 2∘× 2.5∘ horizontal
resolution. Other columns contain the absolute differences from doubling the
transport operator duration to C10T10 (middle), and doubling the chemical
operator duration to C20T05 (right). Each row from top to bottom represents
carbon monoxide (CO), nitrogen oxides (NOx), hydroxyl radical (OH), and
the production of ozone (P[O3]). Simulations are represented as
CccTtt with chemical operator duration, C=cc min, and transport
operator duration, T=tt min. (b) As described in
panel (a), but each row from top to bottom represents ozone
(O3), sulfur dioxide (SO2), sulfate (SO42-), and nitrate
(NO3-).
Sensitivity of simulated species to changes in operator duration
(C20T10 to C10T05) at two different horizontal resolutions over North America
(global 4∘× 5∘, and nested
0.5∘× 0.67∘ simulations). The upper two rows
contain monthly mean ground-level concentrations simulated with the C20T10
operator duration for 4∘× 5∘ (top row) and
0.5∘× 0.67∘ (second row) resolutions. The two lower
rows contain the monthly mean differences (C20T10 minus C10T05) for
4∘× 5∘ (third row) and
0.5∘× 0.67∘ (bottom row) resolutions. Each column
from left to right represents nitrogen oxides (NOx), secondary inorganic
aerosols (SIA), ozone (O3), and carbon monoxide (CO).
Identifying the optimal operator duration
A practical way to select optimal chemical and transport operator durations
is to identify the simulation with the lowest error (Esims)
per unit of computation time. To quantify the simulation accuracy per unit
CPU time, we propose a simple metric, the CPU-time adjusted composite
normalized error (CNE) which represents a tradeoff between the simulation
accuracy and the associated computation expense. This is performed by
normalizing the relative simulation error Esims for species
s by the CPU time t for the simulation under consideration
tsim and for a reference simulation tref, and taking
the mean of the four species.
CNE=14×∑sEsimsErefs×tsimtref
We normalize Esims by the reference Erefs so
that the CPU-time adjusted composite normalized error for each species is of
similar magnitude. The variation of CNE across operator durations is
unaffected by the choice of reference simulation; C10T10 used here. The
relative value of CPU time vs. simulation accuracy is subjective and depends
on scientific objective. This definition of CNE gives equal weighting to the
respective cost of CPU time and simulation accuracy. The simulation with the
lowest CNE is used to identify an optimal chemical and transport operator
duration.
Results and discussion
Figure 1 shows the computational performance for the series of GEOS-Chem
simulations conducted here. The CPU time decreases by factors of 3–5 from
fine to coarse operator duration. The CPU time increases by about a factor of
4 from 4∘× 5∘ to 2∘× 2.5∘
and another factor of 2 to a single nested simulation at
0.5∘× 0.667∘. The linearity from
4∘× 5∘ to 2∘× 2.5∘
implies that grid boxes are sufficiently large that CPU time is proportional
to the number of grid boxes, and that transport integration time steps
constrained by the Courant–Freidrich–Lewy criterion (Courant et al., 1967)
are largely unaffected by changes to grid box size at these resolutions.
Comparison of individual CPU times for chemical and transport operators shows
that performing a single cycle of all chemical operations takes
∼ 4 times that of a single cycle of transport operations at the global
scale. This factor is reduced for nested simulations due in part to the
additional CPU time for simulating boundary conditions.
Figure 2 illustrates the sensitivity of the simulations to chemical and
transport operators at 2∘× 2.5∘ horizontal
resolution. The left column shows the species concentrations for the “true”
simulation (C10T05). The middle column shows the difference in species
concentrations from doubling the transport operator duration. This doubling
is in practice a change in time truncation of the transport operator from T×C×T×T×C×T to T×C×T×C since the transport operator must keep pace with the chemistry operator.
Increasing the transport operator duration tends to increase concentrations
of emitted species like CO and NOx over source regions since species are
more uniformly mixed by long continuous operator durations before loss
processes such as dry deposition and chemistry occur. More homogeneous fields
have lower dry deposition rates as a larger fraction is mixed aloft, and
lower chemical loss rates depending on the chemical regime. The increase in
CO over source regions is partly associated with decreases in OH. Increasing
concentrations of ozone precursors increases ozone production (P[O3]).
Wild and Prather (2006) similarly found that ozone production increases at
coarser horizontal resolution. Increasing the transport operator duration
increases SIA components, especially over the source regions of East Asia,
northern India, and North America.
Relative simulation error of different species
(Esims, Eq. 3) with various operator durations at
2∘× 2.5∘ horizontal resolution. Colored lines and
dots represent the relative simulation error for nitrogen oxides (NOx;
red), secondary inorganic aerosols (SIA; blue), ozone (O3; green), and
carbon monoxide (CO; magenta). Simulations are represented in the abscissa as
CccTtt with chemical operator duration, C=cc min, and transport
operator duration, T=tt min.
The right column in Fig. 2 shows the change in species concentrations from
increasing the chemical operator duration. Hydroxyl radical concentrations
increase, NOx concentrations decrease, and P[O3] decreases with
increasing chemical operator durations over source regions. Berntsen and
Isaken (1997) found that the error introduced by coarser chemical operator
durations is higher in polluted regions than the clean background due to the
increased time lag, and invariant production and loss across rapid chemical
cycles. A longer chemical operator duration decreases sulfate and ammonium
but increases nitrate over source regions. Inspection of SO2 and
H2O2 fields indicates that sulfate formation through H2O2
in clouds decreases at longer chemical operator durations. In turn, SO2
and NH3 concentrations increase at longer chemical operator durations
due to the corresponding decreases in ammonium sulfate or ammonium bisulfate.
The additional free ammonia at longer chemical operator durations tends to
promote regional ammonium nitrate formation depending on local
thermodynamics. An increase of total SIA mass with increasing chemical
operator duration is driven by nitrate and ammonium, and partially
compensated by a reduction in sulfate, especially downwind of source regions.
We find similar spatial patterns for other operator duration combinations,
and other horizontal resolutions.
Figure 3 shows the sensitivity of simulated species to changes in operator
duration (C20T10 to C10T05) at two other horizontal resolutions (global
4∘× 5∘, and nested North America 0.5∘× 0.67∘
simulations) considered here. Spatial patterns of monthly mean ground-level
concentrations, and absolute differences are similar, albeit with finer
spatial heterogeneity resolved in the nested simulation. However, some
resolution dependent differences do arise reflecting nonlinear feedbacks.
Effect on simulated species of changing from the GEOS-Chem
traditional operator durations (C30T15) to the shortest operator durations
considered (C10T05). The top row contains monthly mean ground-level
concentrations simulated with the C30T15 operator duration at
2∘× 2.5∘ horizontal resolution. The next two rows
contain the monthly mean differences (C30T15 minus C10T05) for absolute
(second row) and relative (third row) differences. The two lowest rows
contain the maximum differences (C30T15 minus C10T05) for absolute (fourth
row) and relative (bottom row) differences. Each column from left to right
represents nitrogen oxides (NOx), secondary inorganic aerosols (SIA),
ozone (O3), and carbon monoxide (CO).
Figures 4 shows the relative simulation error for nitrogen oxides, secondary
inorganic aerosols, ozone and carbon monoxide with varying operator durations
at 2∘× 2.5∘ horizontal resolution. Relative
simulation errors for all these major species increase by more than a factor
of 5 from the shortest to longest operator duration. Errors increase fairly
smoothly with increasing chemical and transport operator duration until the
transport operator duration exceeds 30 min. Then errors increase by an order
of magnitude for long lived species of O3 and CO. The saw-tooth pattern
for CO vs. O3 reflects a greater sensitivity of CO to transport operator
duration and a greater sensitivity of O3 to chemical operator duration.
Relative simulation errors for other horizontal resolutions follow similar
pattern. These relative errors of 5–35 % for NOx and SIA are
comparable to typical model–observation errors of ∼ 30 % for
NOx (Boersma et al., 2008; Hudman et al., 2007) and 20–40 % for SIA
(Philip et al., 2014; Heald et al., 2012). Operator duration errors of
< 2 % for O3 and CO are smaller than typical
model–observation errors of ∼ 20 % for ozone (Zhang et al., 2011;
Wang et al., 2009) and 10–20 % for CO (Duncan et al., 2007; Shindell et
al., 2006).
Figure 5 shows the difference in simulated species at 2∘× 2.5∘ horizontal resolution for the GEOS-Chem traditional (C30T15) minus the
finest operator durations considered (C10T05). The spatial variation for the
monthly mean ground-level concentrations is generally within 5–15 % for
short lived species like NOx and SIA, and within 1 % for longer lived
species like O3 and CO. Santillana et al. (2016) similarly found an
upper limit of 10 % for operator splitting errors. However, the maximum
hourly spatial variation can exceed 50 % for short lived species and 5 %
for longer lived species. The spatial pattern of extrema resembles that of
the monthly mean, albeit with more heterogeneity from synoptic variation.
We also examined the diurnal variation and vertical profile of extrema.
Extrema arise from all times of day with a slight tendency for larger values
for NOx at night, for O3 near sunrise and sunset, and for SIA
and CO near noon. Zonal mean vertical profiles exhibit largest differences
in the lower troposphere for NOx and SIA, with more homogeneous
differences throughout the troposphere for O3 and CO. Near the
subtropical jets of the upper troposphere O3 and CO have maximum
extrema of up to 3 %.
CPU-time adjusted composite normalized error (CNE, Eq. 4) for
GEOS-Chem simulations with various horizontal resolutions and operator
durations. Colored lines and dots represent the CNE for the global
simulations at 4∘× 5∘ (red) and
2∘× 2.5∘ (blue), and the nested simulations at
0.5∘× 0.667∘ (green) horizontal resolutions. Error
bars represent standard error in CPU time. Simulations are represented in the
abscissa as CccTtt with chemical operator duration, C=cc min, and
transport operator duration, T=tt min.
Figure 6 shows the CPU-time adjusted composite normalized error for the
GEOS-Chem simulations at various horizontal resolutions and operator
durations. The CNE is significantly higher with C=T than C=2×T. We confirmed this tendency with different choices of “truth” (such as
C05T05, C10T10) or reference (such as C10T05) simulations. This finding
motivates the traditional approach of using C=2×T in GEOS-Chem
simulations. Applying the chemical operator as frequently as the transport
operator (with C=T) appears to increase computation cost with little
benefit in accuracy. The CNEs for all three horizontal resolutions have noisy
minima with a chemical operator duration of 20 min and a transport operator
duration of 10 min (C20T10). A unit of computation time has a similar
efficiency for a small range of operator durations from 10 to 20 min. We
found similar patterns in the variation of CNE with operator durations with
CNE calculated for selected domains, such as over the Northern Hemisphere,
nested model regions, land grid boxes, and over the entire troposphere. We
conducted additional simulations at 4∘× 5∘
horizontal resolution for January 2011 with a spin-up of 7 months, and found
similar patterns in CNE.
Comparison of mean∗ relative simulation error vs.
horizontal resolution, with “truth” defined at
2∘× 2.5∘ horizontal resolution.
The relative simulation error decreases by 40–50 % (Fig. 4) by changing
the operator duration from the traditional (C30T15) to the optimal (C20T10)
at 2∘× 2.5∘ horizontal resolution. The relative spatial
variations are < 20 % for NOx and SIA, and < 1 %
for O3 and CO. However, the CPU time increases by 20 % by the
decrease in operator duration.
Table 1 shows the relative simulation error at 4∘× 5∘
horizontal resolution with “truth” at 2∘× 2.5∘ resolution
(C10T05) to investigate the tradeoff between horizontal resolution and
operator duration. The simulation error for all species at 4∘× 5∘
resolution increases by an order of magnitude compared to 2∘× 2.5∘ resolution for any choice of operator duration tested here.
The error in this configuration is insensitive to operator duration, and
dominated by representativeness differences due to spatial structure
resolved at 2∘× 2.5∘ resolution, but not at 4∘× 5∘ resolution. Nonlinear chemistry at different horizontal resolutions
(e.g., Wild and Prather, 2006) also plays a role. Numerical errors due to
advection processes generally exceed those from operator splitting (e.g.,
Prather et al., 2008; Santillana et al., 2016). We therefore recommend
prioritizing horizontal resolution over operator duration for offline CTMs
using time-averaged meteorological fields as tested here. As meteorological
fields used in CTMs become available at finer temporal and spatial
resolution, the value of shorter operator duration should further increase.
We encourage CTM users to specify in publication the duration of operators
due to its effect on simulation accuracy.
Conclusions
The computational expense of chemistry-transport models warrants
investigation into their efficiency and accuracy. Solving the continuity
equation in CTMs through operator splitting method offers numerical
efficiency, however, few studies have examined the implications of operator
duration on simulation accuracy. We conducted simulations with the GEOS-Chem
model for multiple choices of operator duration from 10 to 60 min as
typically used by global CTMs. We found that longer continuous transport
operator durations increase ozone precursors and ozone production over
source regions since a more homogeneous distribution reduces loss through
chemical reactions and dry deposition. Longer chemical operator durations
decrease NOx and ozone production over source regions. Longer chemical
operator durations reduce sulfate and ammonium concentrations, however
increase nitrate due to feedbacks with in-cloud SO2 oxidation and local
aerosol thermodynamics.
We investigated the computational efficiency with the GEOS-Chem model, and
found that the simulation computation time decreases by up to a factor of 5
from short (C10T05) to long (C60T60) operator duration. The chemical operator
consumes about 4 times the CPU time of the transport operator. We
subsequently compared the root mean square differences in the ground-level
concentrations of nitrogen oxides, secondary inorganic aerosols (SIA), ozone
and carbon monoxide with a finer temporal or spatial resolution taken as
“truth”, and estimated the relative simulation error. The relative
simulation error for these species increases by more than a factor of 5 from
the shortest to longest operator duration. Monthly mean simulation errors of
about 30 % for NOx and SIA from long operator duration are
comparable to typical model–observation errors, while simulation errors for
CO and O3 tend to be less than 2 % for operator duration
< 30 min.
In order to account for simulation accuracy with computational cost, we
proposed a metric, CPU-time adjusted composite normalized error that
identifies the operator duration with respect to CPU cost. We find greater
efficiency of using C=2×T than C=T for all horizontal
resolutions. The composite normalized error exhibits a noisy minimum for a
chemical operator duration of 20 min and transport operator duration of
10 min for the range of operator durations and horizontal resolutions
considered here. Nonetheless, the relative simulation error from changing
horizontal resolution exceeds that from changing operator durations within a
horizontal resolution. We recommend prioritizing fine spatial resolution
before considering different operator durations in offline CTMs with
time-averaged archived meteorological fields as tested here. The importance
of shorter operator durations should increase with the availability of
time-averaged meteorological fields at higher temporal resolution. Short
operator durations could offer even greater benefits to simulation accuracy
in online CTMs that offer meteorological fields at temporal resolutions
closer to operator duration. We encourage CTM users to specify in
publications the durations of operators due to their effects on simulation
accuracy.
Code availability
The GEOS-Chem code is freely accessible to the public, by following the
guidelines in http://wiki.geos-chem.org/. This work used
GEOS-Chem version 10-01.
Acknowledgements
We thank Colette Heald, Daniel Jacob and Patrick Kim for useful comments at
the early stages of this research. We are grateful to three anonymous
reviewers for helpful comments. This work was supported by the National
Science and Engineering Research Council, Canada, and the Atlantic
Computational Excellence Network
(http://www.ace-net.ca/). Edited by:
A. Kerkweg
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