The Community Multiscale Air Quality (CMAQ) model (Byun and Schere, 2006) is a sophisticated, 3D Eulerian (gridded) numerical modeling system based on message passing interface (MPI) that uses scientific first principles to simulate the chemical transformation and transport of ozone, particulate matter, toxic compounds, and acid deposition. Since the formation and transformation of chemical species are functions of complex atmospheric and chemical interactions, two primary input types are required to initialize CMAQ simulations: meteorology and emissions. First, meteorological data (such as temperature, wind, cloud formation, and precipitation rate) provide atmospheric conditions to drive CMAQ. The second required input field, which is the focal point of this study, is emission data (i.e., emission rates from emission sources) that characterize pollutants from both man-made and naturally occurring sources.

The CMAQ model typically requires multiple emission datasets which occupy a significant amount of disk space. Although disk space is becoming progressively cheaper and more affordable, the research and computational needs are rapidly increasing and becoming more complex. For instance, the total sizes of emission and meteorological datasets are about 7.0 and 6.8 GB, respectively, for a 1 d CMAQ simulation for the contiguous United States (CONUS) with a horizontal resolution of 12 km. The total disk-space size for 1 d of output is 20 GB (for a typical output configuration considering only surface output and neglecting extra diagnostic output). Including 3D fields and diagnostic output, however, the total output disk-space size can easily be tripled. Most studies with CMAQ on this scale create at least a full year's worth of data, so aggressive disk-space management is justifiable to minimize overall costs associated with running CMAQ. Aggressive disk-space management could be a substantial cost-saving measure, regardless of whether simulations are conducted on-site (such as with a high-performance computing architecture or a Linux cluster) or by using cloud computing, where data retrievals can quickly elevate costs. Here, we propose optimizing disk space by compressing CMAQ emission datasets as one practical consideration to maximize storage capacity. If successful, this option could be extended to other input types with large disk-space needs, such as meteorological data.

Compression algorithms can be described as either lossless or lossy. Lossless compression algorithms reduce disk space by replacing repeated sequences with a smaller, unique identifier. Thus, an entire dataset can be retrieved, once uncompressed, without alteration of the original dataset (hence the name, lossless). Lossy algorithms, however, in terms of numeric arrays, reduce disk space by manipulating the mantissa of individual floating-point numbers. Typically, trailing, or insignificant bits, are replaced with a sequence of zeros or ones. As a result, data are compressed at the cost of numerical inconsistencies between the original dataset and the compressed dataset.

The concept of maximizing disk space by altering netCDF datasets has been examined previously by Zender (2016) and Kouznetsov (2021). Zender (2016) created a versatile toolset that compresses data based on user specifications that are applied to the mantissa of floating-point datasets. The first notable algorithm developed by Zender (2016) is precision trimming, which is publicly available in the netCDF operators (NCOs, http://nco.sourceforge.net/nco.html, last access: 11 April 2022) utility. Precision trimming sets all non-significant bits to zero (bit shaving) which, based on analysis, produces an undesirable bias of the compressed data (Zender, 2016). As a result, Zender (2016) introduced a Bit Grooming algorithm (default algorithm in the NCO) that shaves (to zero) and sets (to one) the least significant bits of consecutive values. Despite the additional toolset, Kouznetsov (2021) found substantial artifacts, or numerical inconsistencies, in multipoint statistics caused by Bit Grooming. Due to the suboptimal results, Kouznetsov (2021) developed and evaluated multiple lossy compression algorithms with respect to the NCO's available toolsets from Zender (2016). Kouznetsov (2021) created a round and half-shaved lossy compression algorithm which both doubled compression accuracy by rounding the mantissa to the nearest value that has zero tail bits and by setting all tail bits to zero, except for the most significant bit which gets set to one (Kouznetsov, 2021).

Excluding analyses conducted on datasets via lossy compression algorithms, the authors are unaware of any studies that have been conducted on the compression efficiency of floating-point datasets with respect to n significant digits. Additionally, Zender (2016) and Kouznetsov (2021) did not conduct evaluations regarding the impact of altered precision datasets on numerical simulations. In this study, the precision of netCDF datasets will be reduced and compressed to explore compression efficiency, and the resultant reduced precision datasets will be used to run CMAQ simulations to quantify the impacts on runtime and on model accuracy as a result of dataset manipulation via a lossy compression algorithm. This study proceeds as follows: in Sect. 2, a description of the methodology will be provided, followed by results in Sect. 3 and then the conclusions in Sect. 4.

All input and output files in this study are 32-bit, binary, netCDF files which inherently contain seven or eight significant digits at most. To perform this study, we created a simple tool written in Fortran to truncate floating-point data in netCDF files by keeping n significant digits which are normalized in scientific notation. Table 1 shows several examples of this numerical manipulation. We applied this tool to alter the precision of two different datasets (input emission and CMAQ model output) by keeping n significant digits.

For this study, CMAQ v5.3.1 (USEPA, 2019; Appel et al., 2021) was run with 459 columns, 299 rows, and 35 vertical layers with a horizontal grid-scale resolution of 12 km (Fig. 1a). Emission input files consist of two area sources and nine point sources (hourly). The area-source emission files contain 57 and 62 variables, and the point-source files contain anywhere from 54 to 58 variables (containing one vertical layer). Ten CMAQ output files (nine of them are hourly) were generated in this study: three output files were generated for simulation-restart purposes (SOILOUT, CGRID which contains only 1 h data, and MEDIA), two files contained average (APMDIAG and ACONC) and hourly (CONC) species concentrations, three files held wet deposition (WETDEP1; 140 variables), dry deposition (DRYDEP; 174 variables), and deposition velocity (DEPV; 104 variables) output, and lastly, the final file contained biogenic emission diagnostic output (B3GTS).

In total, we conducted four annual CMAQ simulations for 2016: one with unaltered emission data (simulation orig) and three with altered precision emission data by setting n to five (A05), four (A04), and three (A03) for all emission input files (gridded_no_rwc, gridded_rwc, ptnonipm, ptegu, ptagfire, ptfire, ptfire_othna, pt_oilgas, cmv_c3_12, cmv_c1c2_12, and othpt) utilized by CMAQ for this study. On the output side, direct CMAQ outputs (ACONC, APMDIAG, DRYDEP, and WETDEP1) from the A05, A04, and A03 (in which A0n signifies an altered simulation which utilized altered precision emission data to n significant digits) simulations were similarly altered to possess five, four, or three significant digits (denoted as FX05, FX04, and FX03, respectively, in which FX0n signifies an altered precision case which was post-processed by an A0n simulation's CMAQ output). Emission input and CMAQ output data were then compressed separately by gzip (GNU Gzip, https://www.gnu.org/software/gzip, last access: 11 April 2022) and bzip2 (https://www.sourceware.org/bzip2, last access: 11 April 2022) for all simulations and cases to determine compression efficiency in terms of the reduction of disk space. In summary, there are four separate simulations (called orig or abbreviated as A0n) and nine additional, altered precision output cases (abbreviated as FX0n). For example, a CMAQ simulation that was run with emission data that were processed with n equals five significant digits, then post-processed to possess three significant digits, is denoted as A05FX03 (see Table 2 for a full list of simulations and cases).

Simulated numerical, or predictive, accuracy was analyzed against concentrations of particulate matter with diameter less than 2.5 µm (PM2.5), ozone (O3), ammonia (NH3), the wet-deposition rates of sodium (Na), ammonium (NH4), chlorine (Cl), nitrate (NO3), sulfate (SO4), and the dry-deposition rate of O3 for all simulations and cases. PM2.5 and O3 were evaluated at in situ stations from the dataset of the United States Environmental Protection Agency's (US EPA) Air Quality System (AQS; Fig. 1b). Ammonia (NH3) was evaluated at in situ stations utilizing observations from the Ammonia Monitoring Network (AMON; Fig. 1c). Hourly observations of O3 were processed to calculate the maximum 8 h daily average concentrations (MDA8) and paired in space and time with calculated MDA8 O3 from post-processed CMAQ output. Likewise, daily averaged PM2.5 observations and 2-week-averaged NH3 observations were used to evaluate CMAQ. Observed values are paired with the volume-averaged pollutant estimate from CMAQ's surface layer's grid cell containing the air quality monitoring site (i.e., nearest neighbor). Statistical metrics were also calculated by pairing gridded values from the orig simulation (considered observed values) and the altered precision simulations and cases (considered the predicted values). Tabulated statistical metrics for grid–grid pairing was computed by taking the mean of hourly, statistical metrics.

Typical statistical metrics including mean bias (MB), correlation coefficient (r), root mean square error (RMSE), and normalized mean bias (NMB) are used to evaluate all chemical species in this analysis at different temporal intervals and for different pairing methodologies (either grid–point or grid–grid) which includes regional stratification (based on regions from Fig. 1a) for several figures. The utilized statistical metrics are denoted below in Eq. () through Eq. (): 1MB=1N⋅∑i=1NYi-Xi,2r=1N-1⋅∑i=1NXi-X‾⋅Yi-Y‾σX⋅σY,3RMSE=∑i=1NYi-Xi2N,4NMB=∑i=1NYi-Xi∑i=1NXi⋅100%, where N is the total number of observed and predicted pairs, X is the observed value, Y is predicted value, σ is the sample standard deviation of a distribution, and the overbars in Eq. () refer to the sample mean of a distribution. Although many compression toolsets exist and optimization is dependent on multiple factors (Kryukov et al., 2020), gzip and bzip2 are the most public, reliable, and widely used compressors. Both utilities are lossless compression algorithms which are available for Linux users. In terms of functionality, gzip uses a compression algorithm called Deflate (Deutsch, 1996) which reduces sequences of datasets by incorporating a combination of LZ77 dictionary coding (Ziv and Lempel, 1977) and Huffman entropy coding (Huffman, 1952). In comparison, bzip2 uses the Burrows–Wheeler (Burrows and Wheeler, 1994) algorithm which sorts all possible rotations of an input lexically and forms an output by concatenating the last character from the sorted list. In terms of compression ratio, bzip2 is notably better than gzip, however, with respect to compression speed, gzip is significantly faster than bzip2. Due to their availability and efficiency, both gzip and bzip2 are utilized in this study (default settings).

We have demonstrated that altering data by keeping a specified number of significant digits in terms of emission input and/or simulated output, increased compression efficiency based on two different, popular compression utilities (gzip and bzip2). For emission data, bzip2 performed far better than gzip and provided compression reduction, on average, by 6 %, 25 %, and 48 %, and 19 %, 47 %, and 69 % for output data for the A05, A04, and A03 cases, respectively, compared to the orig case. In terms of daily simulation runtime for the entire simulation year, the A05, A04, and A03 simulations were faster than the orig simulation in an undedicated HPC system for most simulation days.

As for accuracy, results for all studied simulations, either with altered precision emission only, or with altered precision emission plus altered precision output, produced numerically insignificant differences. For example, the maximum absolute, bulk statistical difference between the orig simulation and the altered cases and simulations for daily PM2.5, MDA8 O3, and 2-week-averaged NH3 did not exceed 1.4×10-4, 3.6×10-5, 1.1×10-1, and 5.3×10-3 µg m-3 or ppb for bias, RMSE, minima, and maxima, respectively. Similarly, a small range in values is replicated for all other bulk statistical metrics such as MB, r, and RMSE. Results stratified by region and season are similar to those for bulk statistics. Based on the in situ evaluation, simulation performance is very similar amongst all cases, with visible differences for the A03 simulation and the FX03 cases in which error is spatially detected in Figs. 7–9.

Statistical inconsistencies arise when comparing grid–grid values of hourly PM2.5, O3, and NH3 versus the orig simulation. Results indicate that similarities amongst the orig simulation decreases with fewer significant digit simulations and cases when analyzing the stacked and stratified (region and season) RMSE bar plot (Fig. 6). More specifically, performance with respect to the orig simulation is worse for the A03 simulation and for the FX03 cases as well. Such discrepancies do not occur consistently based on results provided by bar plots of statistical metrics of deposition rates (Fig. 10). Instead, errors appear to be confined to source regions at specific instances based on the maximum absolute (hourly) error spatial plots with respect to the orig simulation (Figs. 7–9).

In summary, altering datasets by truncation to retain fewer significant digits significantly improved data compression and slightly improved runtime. Based on the thorough, yet spatially limited, in situ evaluation, this study has shown this proposed technique did not compromise model accuracy based on an evaluation of simulations and cases at in situ locations compared to current air quality thresholds for daily PM2.5, MDA8 O3, and 2-week-averaged NH3. These results show the optimal benefit of altering CMAQ input data by keeping three significant digits, then subsequently keeping four significant digits for CMAQ output data. In addition, this proposed technique could be beneficial for groups that perform complex air quality modeling and want to improve disk-space management while negligibly impacting the accuracy of the simulations. Based on the success of this study, we propose testing these techniques on the rest of CMAQ input files such as initial conditions, boundary conditions, and meteorological data to determine the viability of these techniques to more adeptly manage disk space without compromising the quality of the CMAQ simulations used for research and to develop air quality management strategies.