Sensitivity of Chemistry-Transport Model Simulations to the Duration of Chemical and 1 Transport Operators : A Case Study with GEOS-Chem v 1001 2 3

17 Chemistry-transport models involve considerable computational expense. Fine temporal 18 resolution offers accuracy at the expense of computation time. Assessment is needed of the 19 sensitivity of simulation accuracy to the duration of chemical and transport operators. We conduct 20 a series of simulations with the GEOS-Chem chemistry-transport model at different temporal and 21 spatial resolutions to examine the sensitivity of simulated atmospheric composition to operator 22 duration. Subsequently, we compare the species simulated with operator durations from 10 min to 23

60 min as typically used by global chemistry-transport models, and identify the operator durations 24 that optimize both computational expense and simulation accuracy. We find that longer continuous 25 transport operator duration increases concentrations of emitted species such as nitrogen oxides and 26 carbon monoxide since a more homogeneous distribution reduces loss through chemical reactions 27 and dry deposition. The increased concentrations of ozone precursors increase ozone production 28 with longer transport operator duration. Longer chemical operator duration decreases sulfate and 29 ammonium but increases nitrate due to feedbacks with in-cloud sulfur dioxide oxidation and 30 aerosol thermodynamics. The simulation duration decreases by up to a factor of 5 from fine (5 31 min) to coarse (60 min) operator duration. We assess the change in simulation accuracy with 32 resolution by comparing the root mean square difference in ground-level concentrations of 33 nitrogen oxides, secondary inorganic aerosols, ozone and carbon monoxide with a finer temporal 34 or spatial resolution taken as "truth". Relative simulation error for these species increases by more 35 than a factor of 5 from the shortest (5 min) to longest (60 min) operator duration. Chemical operator 36 duration twice that of the transport operator duration offers more simulation accuracy per unit 37 computation. However, relative simulation error from coarser spatial resolution generally exceeds 38 that from longer operator duration; e.g. degrading from 2 o x 2.5 o to 4 o x 5 o increases error by an 39 order of magnitude. We recommend prioritizing fine spatial resolution before considering different 40 operator durations in offline chemistry-transport models. We encourage chemistry-transport model 41 users to specify in publications the durations of operators due to their effects on simulation 42 accuracy. 43 1 Introduction 44 Global and regional chemistry-transport models (CTMs) have a wide range of applications in 45 studies of climate, air quality, and biogeochemical cycling. The last few decades have witnessed 46 CTMs solve the continuity equation for tens to hundreds of chemical species, each with number 70 density n, for individual grid boxes defined in the Eulerian model. 71 (1) 72 ∂n/∂t represents the local temporal evolution of n. nU    represents the transport flux divergence 73 term, where U is the wind velocity vector. P and L are the local production and loss terms 74 respectively. Typically, the above equation is discretized in space, and the continuity equation is 75 simulated as a system of coupled non-linear partial differential equations with chemical and 76 transport operators. These chemical and transport operators are usually simulated sequentially 77 through operator splitting to increase computational efficiency (Hundsdorfer and Verwer, 2003). 78 The transport operator involves solving the 3-D advection equation using efficient numerical 79 schemes (Prather, 1986;Lin and Rood, 1996). Boundary layer mixing, convection, emission and 80 deposition are often simulated as individual operators. The chemical operator representing the 81 temporal evolution of local sources and sinks involves numerically solving a system of coupled 82 ordinary differential equations using efficient solvers (Jacobson and Turco, 1994; Damian et al., 83 2002). The integration timestep in a differential equation solver is important for efficient and 84 accurate solution (Jacobson and Turco, 1994). Moreover, the model accuracy is affected by the 85 duration of chemical and transport operators (Mallet and Sportisse, 2006;Mallet et al., 2007), and 86 the order in which these operators are applied (Sportisse, 2000;Santillana et al., 2016). The 87 operator splitting method requires the coupling between individual operators to be negligible over 88 the operator duration. However, reducing operator durations increases computational expense. 89 Attention is needed to this tradeoff. 90 We examine the sensitivity of a CTM to operator duration by conducting a series of simulations at 91 different horizontal resolutions and operator durations. We then identify the optimal operator 92 (ACENET) Consortium of Canadian Universities (http://www.ace-net.ca/wiki/Glooscap). The 159 operating system is Linux 4.8. We use Intel Fortran compiler version 12. Each GEOS-Chem 160 simulation is submitted as a 16-thread parallelized job on a single node. 161 We calculate the CPU time for the month of July for each operator separately using the Fortran-162 intrinsic routine, CPU_TIME. We found this value identical to the one calculated using the Linux 163 command 'qacct -j'. To reduce the effects of other jobs on the shared cluster, we repeat simulations 164 five times, while excluding data output operations to minimize sensitivity to system input/output, 165 and use the median to represent CPU time. We also report the standard error over the five 166 simulations. 167

Assessing the relative simulation error 168
We treat the simulation with the shortest operator duration as the most accurate. This approach 169 exploits the reduction in error associated with coupling across operators as operator duration 170 diminishes. Assessing simulation error versus operator duration through comparison with 171 observations is impaired by imperfect model processes, by the sparseness of measurements, and 172 by model-observation representativeness biases. We take as "truth" the concentrations simulated 173 with a chemical operator duration (C) of 10 minutes and a transport operator duration (T) of 5 174 minutes (represented as C10T05). Finer resolutions are computationally prohibitive. We define the 175 relative simulation error s sim E captures the variation of a species s from the "true" simulation.

184
We focus on four key species relevant to atmospheric chemistry, namely nitrogen oxides (NOx = 185 NO + NO2), secondary inorganic aerosols (SIA: sum of sulfate, nitrate and ammonium), ozone 186 (O3), and carbon monoxide (CO). These species represent a range of lifetimes from a day (NOx) 187 to weeks (CO). The focus on SIA is designed to devote more attention to chemically active species 188 than to mineral dust and sea salt. We sample the instantaneous values of simulated ground-level 189 concentrations of these atmospheric species every 60 min to span the diurnal variation of chemical 190 environments. We focus on concentrations in July near the Earth's surface when and where 191 chemical and transport timescales tend to be short. 192

Identifying the optimal operator duration 193
A practical way to select optimal chemical and transport operator durations is to identify the 194 simulation with the lowest error ( Berntsen and Isaken (1997) found that the error introduced by coarser chemical operator durations 240 is higher in polluted regions than the clean background due to the increased time lag, and invariant 241 production and loss across rapid chemical cycles. A longer chemical operator duration decreases 242 sulfate and ammonium but increases nitrate over source regions. Inspection of SO2 and H2O2 fields 243 indicates that sulfate formation through H2O2 in clouds decreases at longer chemical operator 244 durations. In turn, SO2 and NH3 concentrations increase at longer chemical operator durations due 245 to the corresponding decreases in ammonium sulfate or ammonium bisulfate. The additional free 246 ammonia at longer chemical operator durations tends to promote regional ammonium nitrate 247 formation depending on local thermodynamics. An increase of total SIA mass with increasing 248 chemical operator duration is driven by nitrate and ammonium, and partially compensated by a 249 reduction in sulfate, especially downwind of source regions. We find similar spatial patterns for 250 other operator duration combinations, and other horizontal resolutions. 251 The relative simulation error decreases by 40-50% (Fig. 4) by changing the operator duration from 299 the traditional (C30T15) to the optimal (C20T10) at 2 o x 2.5 o horizontal resolution. The relative 300 spatial variations are <20% for NOx and SIA, and <1% for O3 and CO. However, the CPU time 301 increases by 20% by the decrease in operator duration. 302 Table 1  resolution over operator duration for offline CTMs using time-averaged meteorological fields as 312 tested here. As meteorological fields used in CTMs become available at finer temporal and spatial 313 resolution, the value of shorter operator duration should further increase. We encourage CTM users 314 to specify in publication the duration of operators due to its effect on simulation accuracy. 315

Conclusions 316
The computational expense of chemistry-transport models warrants investigation into their 317 efficiency and accuracy. Solving the continuity equation in CTMs through operator splitting 318 method offers numerical efficiency, however, few studies have examined the implications of 319 operator duration on simulation accuracy. We conducted simulations with the GEOS-Chem model 320 for multiple choices of operator duration from 10 min to 60 min as typically used by global CTMs. 321 We found that longer continuous transport operator durations increase ozone precursors and ozone 322 production over source regions since a more homogeneous distribution reduces loss through 323 chemical reactions and dry deposition. Longer chemical operator durations decrease NOx and 324 ozone production over source regions. Longer chemical operator durations reduce sulfate and 325 ammonium concentrations, however increase nitrate due to feedbacks with in-cloud SO2 oxidation 326 and local aerosol thermodynamics. 327 We investigated the computational efficiency with the GEOS-Chem model, and found that the 328 simulation computation time decreases by up to a factor of 5 from short (C10T05) to long 329 (C60T60) operator duration. The chemical operator consumes about four times the CPU time of 330 the transport operator. We subsequently compared the root mean square differences in the ground-331 level concentrations of nitrogen oxides, secondary inorganic aerosols (SIA), ozone and carbon 332 monoxide with a finer temporal or spatial resolution taken as "truth", and estimated the relative 333 simulation error. The relative simulation error for these species increases by more than a factor of 334 5 from the shortest to longest operator duration. Monthly mean simulation errors of about 30% for 335 NOx and SIA from long operator duration are comparable to typical model-observation errors, 336 while simulation errors for CO and O3 tend to be less than 2% for operator duration < 30 min. 337 In order to account for simulation accuracy with computational cost, we proposed a metric, CPU-338 time adjusted Composite Normalized Error that identifies the operator duration with respect to 339 CPU cost. We find greater efficiency of using C = 2 x T than C = T for all horizontal resolutions.