Required meteorological inputs include pressure, temperature, and water vapor content. Several options are available to drive the various photolysis schemes (described further below), including direct input of observed photolysis frequencies (J values), solar zenith angles, or an actinic flux spectrum. Concentrations for each chemical species within a given mechanism can be initialized and/or constrained to observations or user-specified values; the default initial concentration is 0. The way chemical constraints are handled depends on the specific scenario. Any constrained species can be held constant throughout a model step, which may be desirable when simulating diurnal cycles using discrete observations (Sects. 3.3 and 3.4). Alternatively, concentrations can be initialized at the beginning of a step and allowed to evolve over time, which may be more appropriate when modeling laboratory experiments or Lagrangian plumes (Sects. 3.1 and 3.2).

A special option is available to force total NOx (= NO + NO2) to input values at the beginning of each step. This provides a means of replenishing NOx without perturbing the modeled NO / NO2 ratio, which may be desirable, e.g., for diurnal cycles of radical chemistry. Figure 1 compares predicted and observed NOx mixing ratios for a diurnal cycle simulation using this option (see Sect. 3.2 for details). For this particular example, daytime NO is slightly overpredicted, while NO2 is underpredicted, which could be related to the model NO2 photolysis frequency (which is not measurement-constrained). Total model NOx is lower than observations by 2 ± 4 % on average. When using this option, it is preferable to keep the model step interval significantly smaller than the NOx lifetime to minimize NOx loss over the course of a step. In this example the step interval is 15 min and the mid-day NOx lifetime is on the order of hours.

Photolysis frequencies control radical production and the lifetimes of numerous compounds. Accurate simulation of J values is challenging due to the variety of factors that influence the radiation field, many of which are often unknown or require some effort to determine (e.g., surface albedo, overhead ozone column, cloud and aerosol extinction or enhancement). F0AM provides three options for calculating J values: bottom-up, MCM, and hybrid.

In the “bottom-up” method, J values are calculated by integrating the product of a user-specified actinic flux spectrum with literature-derived cross sections and quantum yields. Cross sections and quantum yields are taken from the latest IUPAC (Atkinson et al., 2004, 2006) and JPL (S. P. Sander et al., 2011) recommendations when available, and all sources are documented in a single spreadsheet. Spectra, cross sections and quantum yields are convolved using a trapezoidal integration algorithm identical to that employed in NCAR's Tropospheric Ultraviolet and Visible radiation model (TUVv5.2, available at https://www2.acom.ucar.edu/modeling/tropospheric-ultraviolet-and-visible-tuv-radiation-model). This option is most useful when simulating photochemical chamber experiments with non-solar light sources.

The Master Chemical Mechanism (MCM) provides a trigonometric parameterization based on solar zenith angle (SZA). J=Icos⁡(SZA)mexp⁡(-nsec(SZA)) Here, I, m, and n are constants unique to each photolysis reaction, derived from least-squares fits to J values computed with fixed solar spectra and literature cross-section and quantum yields. As discussed in Jenkin et al. (1997) and Saunders et al. (2003), solar spectra underlying this parameterization were calculated from a two-stream radiative transfer model for clear sky conditions on 1 July at a latitude of 45∘ N and an altitude of 0.5 km. Cross sections and quantum yields generally follow IUPAC recommendations as documented on the MCM website (http://mcm.leeds.ac.uk/MCM/). When using this option with a chemical mechanism other than the MCM, photolysis frequencies for reactions not included in the MCM are calculated using the “hybrid” method (below) with a fixed altitude of 0.5 km, overhead ozone column of 350 DU and surface albedo of 0.01. The ozone column and albedo are chosen to optimize agreement between the MCM and hybrid values of J(NO2) and J(O(1D)).

The “hybrid” method is essentially an extension of the bottom-up method, combining cross sections and quantum yields from the latter with solar spectra derived from TUVv5.2. A total of 20 064 solar spectra were calculated offline over a range of SZA (minimum/increment/maximum of 0/5/90∘), altitude (0/1/15 km), overhead ozone column (100/50/600 DU), and albedo (0/0.2/1) values. J values calculated for all solar spectra are organized into a set of lookup tables. At the start of a model run, input SZA, altitude, ozone column, and albedo are used for linear interpolation across these tables. This method extends the number of available photolysis frequencies well beyond those included in the MCM parameterization while avoiding the computational expense of running the full TUV model inline. Also, the hybrid method is fully traceable: cross sections and quantum yields are documented in a single file, and both TUV-derived actinic fluxes and the code for calculating J value lookup tables are available upon request.

Figure 2 compares photolysis frequencies calculated with the MCM parameterization and the F0AM hybrid method for a single set of inputs (SZA = 0∘, altitude = 0.5 km, albedo = 0.01, O3 column = 350 DU). The overhead O3 column and albedo for this comparison are chosen to optimize average agreement between the hybrid and MCM values, since the exact solar spectra underlying the MCM parameterization are not available. The two methods agree to within ±20 % for inorganics, organic nitrates and some VOCs. Agreement is more variable for larger VOCs, in part due to varying quantum yields; for example, MCM uses different branching ratios for the glyoxal photolysis channels than those recommended by JPL or IUPAC. Figure 2 also compares hybrid values with those output directly by TUVv5.2, which includes its own photolysis algorithm. Photolysis frequencies for these two methods generally agree to within ±20 %, as expected since both utilize identical solar spectra and generally comparable cross sections and quantum yields. Differences for N2O5, CH3CHO, and MEK photolysis stem from the choice of quantum yields. Differences for C2H5CHO and CH3COCH3 photolysis are due to known errors in TUVv5.2 that will be resolved in the next release (S. Madronich, personal communication, 2016). Based on the above comparison, we recommend the hybrid method over the MCM parameterization for most “real atmosphere” simulations.

Any J value can be constrained to observations via direct input. It is also possible to specify a scaling factor for all parameterized J values. Typically this scaling is taken as the ratio of an observed photolysis frequency to its model-calculated value. Scaling to observed values is encouraged when working with field observations, as neither the MCM or hybrid methods capture the full extent of atmospheric properties that can influence solar radiation. For example, in the steady-state simulation discussed in Sect. 3.4, removing observation-based constraints on J(NO2) and J(O1D) increases average calculated NO, OH, and HCHO mixing ratios by 34, 40, and 11 %, respectively.

Table 1 lists the gas-phase chemical mechanisms currently available with F0AM. The MCM is a prevalent explicit mechanism, and version 3.3.1 (Jenkin et al., 2015) contains numerous updates to reflect recent laboratory and theoretical advances. MCMv3.2 (Saunders et al., 2003) is included for comparison purposes. Several MCM extensions are also available, including simplified monoterpene and sesquiterpene oxidation (Wolfe and Thornton, 2011), chlorine–VOC reactions (Riedel et al., 2014), and a subset of bromine and chlorine reactions from MECCA (R. Sander et al., 2011). The Carbon Bond mechanisms, CB05 (Yarwood et al., 2005) and CB6r2 (Hildebrandt Ruiz and Yarwood, 2013), and the Regional Atmospheric Chemistry Mechanism version 2 (RACM2) (Goliff et al., 2013) are condensed mechanisms commonly used in regional air quality applications. The version of the GEOS-Chem mechanism included with F0AM is based on GEOS-Chem v9-02 (Mao et al., 2013) with updates to isoprene chemistry as described in several recent publications (Fisher et al., 2016; P. S. Kim et al., 2015; Marais et al., 2016; Travis et al., 2016). Toggling between various mechanisms is straightforward through the setup script. None of the above mechanisms include heterogeneous or aerosol-phase processes.

Chemical rate equations are integrated with MATLAB's ode15s solver, which is designed specifically for stiff systems. A utility is available for converting mechanisms from the FACSIMILE (MCPA Software) format into the F0AM input format, and a similar utility for converting KPP-formatted mechanisms (Damian et al., 2002) may be included in a future release. We hope that the community will continue to add to the F0AM mechanism library and that this model can serve as a platform for inter-comparing and evaluating updates to these mechanisms.

A major shortcoming of the 0-D box modeling approach is the lack of explicit representation of transport processes (entrainment, dilution, etc.), which has several practical consequences. First, primary emissions like NOx and hydrocarbons must be constrained or otherwise re-supplied to compensate for chemical loss. Emissions can also be parameterized explicitly but require knowledge of the boundary layer depth and assumed instantaneous mixing. Second, a generic “physical loss” lifetime of 6–48 h is often assigned to all species to mitigate build-up of long-lived oxidation products over multiple days of integration. Model users must be aware of the limitations imposed by these choices. For example, constraining NO2 is not appropriate when investigating ozone production, and the choice of physical loss lifetime can affect simulated OH reactivity (Edwards et al., 2013; Kaiser et al., 2016).

F0AM adopts a simple parameterization for first-order ventilation: dXdt=-kdilX-Xb. Here, [X] is the chemical concentration, [X]b is a fixed “background” concentration, and kdil is a first-order dilution rate constant. Expansion of Eq. (2) shows that this parameterization is effectively the combination of a zeroth-order source (kdil[X]b) and a first-order sink (-kdil[X]). The choice of kdil and [X]b depends on the particular problem. The dilution rate constant can be set to a constant value or parameterized using additional information, such as the decrease in conserved tracers in evolving plumes (Dillon et al., 2002; Müller et al., 2016), wind speed (Bryan et al., 2012), or boundary layer growth rate (Kaiser et al., 2016). Background concentrations are typically set to up-wind, out-of-plume, or free tropospheric values, depending on the system and available information. Setting [X]b to zero yields a simple first-order sink, analogous to the physical loss lifetime discussed above. Regardless of the application, it is important to justify the choice of kdil and [X]b and/or perform sensitivity simulations to characterize how uncertainties in physical processes impact model interpretation.

Much of the flexibility of F0AM stems from up-front control of how integration proceeds across a single step and between steps. For example, the end points of one step can be used to initialize the next step, or each step can be treated as independent. The former option is appropriate for simulating the time evolution of field observations (which may have time-varying input constraints), while the latter is useful for modeling multiple chamber experiments or performing a sensitivity study (e.g., the effect of varying levels of NOx on isoprene oxidation). A “solar cycle” option is also available to make photolysis frequencies evolve “in real time” over the course of a model step, which is a standard procedure when modeling aircraft observations (Olson et al., 2006). In this case, the user must also specify location and time. It is left to the user to determine the appropriate total integration time – no convergence criteria are incorporated into model execution.

Model output is collected in a single hierarchical structure and includes calculated chemical concentrations and reaction rates, as well as inputs. Outputs can include all intermediate concentrations and rates along each step or values at the end of the step only (specified during setup). Tools are also provided for manipulating and plotting output; some example plots are shown below. One tool of special note is a function to identify MCM species with specific chemical functionalities (carbonyls, nitrates, etc.) using simplified molecular input line entry system (SMILES) strings (Weininger, 1988). This tool is useful for examining groups of compounds (e.g., Fig. 4) and has been used previously to develop a rough deposition parameterization for many MCM species (Kaiser et al., 2016).

Photochemical chambers are a standard tool for isolating and characterizing chemical processes. 0-D models are useful for both planning experiments and interpreting data (e.g., by testing proposed mechanism modifications). Here, we use F0AM with MCMv3.3.1 to predict NOx-dependent yields of several isoprene oxidation products. For these simulations, model meteorology is set to nominal values (298 K, 1000 mbar, 10 % RH). J values are calculated using the “bottom-up” method with a light spectrum corresponding to UV bulbs with output centered at 350 nm (Crounse et al., 2011). The model is initialized with 10 ppb of isoprene, 200 ppb of hydrogen peroxide (a common OH source), and NO2 mixing ratios ranging from 10 ppt to 10 ppb. The model is integrated to 1 h for each initial NO2 concentration, and yields are calculated as the slope of product gained against isoprene lost over minutes 10–15 (see inset in Fig. 3). We do not consider wall losses in this simple example, but such processes are typically represented with additional first-order loss reactions (Wolfe et al., 2012).

Figure 3 shows the yields of three first-generation products that track the fate of isoprene hydroxyperoxy radicals (ISOPO2): methyl vinyl ketone (MVK) and methacrolein (MACR) from the NO channel, isoprene hydroxyhydroperoxides (ISOPOOH) from the HO2 channel, and hydroperoxyaldehydes (HPALD) from unimolecular isomerization. The chemistry shifts from HO2- to NO-dominated at 0.2 ppb of initial NO2. Such plots can help define optimal experiment conditions and strengthen intuition regarding expected relationships in both the laboratory and the real atmosphere.

The time evolution of a plume – from a wildfire, urban core, power plant, or other strong emitter – offers a natural experiment for testing chemical understanding. As an example, we simulate a young biomass burning plume sampled from an aircraft during NASA's DISCOVER-AQ mission (Deriving Information on Surface Conditions from Column and Vertically Resolved Observations Relevant to Air Quality, data available at DOI 10.5067/Aircraft/DISCOVER-AQ/Aerosol-TraceGas). Plume sampling occurred longitudinally from the source to ∼ 13.5 km downwind, corresponding to a processing time of ∼ 1 h. Model setup is identical to that described in Müller et al. (2016). Briefly, gas concentrations are initialized with mixing ratios observed over the first 1 km and include O3, CO, CH4, NO, NO2, HONO, and a suite of 17 reactive VOCs. All gas concentrations are allowed to evolve freely in time. Meteorological conditions are updated every 250 s (roughly every 1 km). The dilution constant is calculated using the observed decay of CO; the dilution lifetime (1/kdil) increases from 6 min to 106 min over the simulation period. Background concentrations are taken from measurements outside the plume. MCMv3.3.1 chemistry is employed using MCM's default photolysis scheme, with additional reactions for initial oxidation of furfural and furan.

Figure 4 illustrates the simulated progression of total oxidized nitrogen (NOy). NOx decreases by over a factor of 2 over the course of an hour, but this is mostly balanced by formation of peroxy nitrates (mainly peroxyacetyl nitrate, PAN) and nitric acid. As presented in Müller et al. (2016), the model quantitatively replicates the observed conversion of NOx to PAN, as well as the formation of ∼ 60 ppb of ozone. The excellent model–measurement agreement for this case suggests that more advanced frameworks that account for Gaussian dispersion (Alvarado and Prinn, 2009) may not always be necessary, but this likely depends on the nature of each case study and available constraints. On the other hand, the model does not capture the increase in some oxidized VOCs, such as formaldehyde, likely indicating some missing VOC precursors. In conjunction with a detailed dataset, a box model can help to characterize the nature of such “missing” reactants and quantify the impact of these compounds on downwind chemistry.

Ground-based field intensives can provide detailed data sets for driving model simulations. Here we use a subset of observations from the 2013 Southeast Oxidants and Aerosol Study (SOAS, data available at http://www.eol.ucar.edu/field_projects/sas). Observations from the Centreville, Alabama, site are averaged over the entire campaign to a diurnal cycle in 1 h intervals. There is substantial day-to-day variability in this dataset, and this coarse averaging procedure is for illustrative purposes only. Chemical constraints include NOx, OH, CO, PAN, and a suite of ∼ 35 VOCs. Total NOx is semi-constrained using the “fixed NOx” option (Fig. 1), and to facilitate this we interpolate the hourly averaged data to a 15 min time base. Ozone is initialized for the first step only. We use MCMv3.3.1 chemistry and the hybrid J value parameterization with a fixed O3 column of 320 DU and albedo of 0.05, without further scaling (no radiation measurements are available). A physical loss lifetime of 24 h (using the dilution parameterization) is applied to all species. The model run extends over 4 days, using the same constraints for each day.

Figure 5a shows the evolution of ozone over the 4-day simulation period. Ozone is in near-steady state by the end of the fourth day; concentrations increase by less than 2 % between days 3 and 4. Ozone growth is rapid in the morning but slows around noon, concomitant with reduced NOx (Fig. 1). The dominant fate of organic peroxy radicals also shifts from reaction with NO to reaction with HO2 at this time (Fig. 5b), which likely also contributes to reduced ozone production (less radical cycling) and may impact production of aerosol precursors, such as epoxides (Paulot et al., 2009b). Through sensitivity simulations that probe the timing of such changes, box modeling facilitates rapid-fire testing of multiple hypotheses and full leveraging of comprehensive datasets.

Despite good model–measurement agreement for peak ozone mixing ratios in the afternoon, significant discrepancies occur at other times. Between hours 07:00 and 12:00 local solar time, observed ozone increases by 23 ppb, while modeled values only increase by 15 ppb. This is likely due to a lack of residual layer entrainment in the model, which can be a significant ozone source in the morning (Su et al., 2016). The model also underpredicts the evening ozone decay rate by a factor of 2, potentially implying inadequate treatment of deposition (dilution is the only physical loss in our setup). These issues highlight some of the challenges of simulating near-surface composition in a complex environment with a relatively simple model. Additional functionality could be added in the future to better represent physical processes.

Regional and global models employ a variety of chemical mechanisms. Box models can isolate the chemistry contribution to inter-model differences and pinpoint potential shortcomings in condensed mechanisms. Here we show an example comparison between all mechanisms included in F0AM (Table 1). Constraints are taken from airborne observations acquired in the Atlanta area during the 12 June 2013 flight of the Southeast Nexus mission (SENEX, data available at http://esrl.noaa.gov/csd/groups/csd7/measurements/2013senex/P3/DataDownload/) (Warneke et al., 2016). Figure 6a shows time series of altitude, NOx, and isoprene mixing ratios for the representative flight segment, which includes (chronologically) a vertical profile, a boundary layer transect downwind of a power plant plume, and a pass through the Atlanta urban core. Chemical constraints include 1 min average observations of CH4, CO, O3, NO2, PAN, methanol, and isoprene. Hybrid J values are corrected by the average ratio of observed-to-calculated J(NO2) and J(O1D). For each 1 min interval, the model is run with a 1 h time step for 5 days in “solar cycle” mode to achieve steady state.

Figure 6b, c, and d compare modeled OH, HO2, and OH reactivity (inverse OH lifetime) for all mechanisms. OH concentrations agree to within ±30 %, and HO2 concentrations and OH reactivity to within 20 %, over the whole period. Even this relatively short simulation is revealing. For example, both the MCM and carbon bond mechanisms exhibit an increase in OH and HO2 between the old and new mechanism versions. The most obvious discrepancy between the chosen mechanisms is the somewhat low value of HO2 for RACM2. To investigate further, we can compare rates of HO2 production and loss between RACM2 and MCMv3.3.1. HO2 lifetimes of 10–50 s are nearly identical for both mechanisms; thus, the difference must be related to production. Figure 7 compares HO2 sources for the two mechanisms. The production of HO2 from OH reactions with HCHO, CO, and other compounds is significantly slower in RACM2. RACM2 OH concentrations, however, fall in the middle of the pack. Furthermore, HOx agreement is much better in the high-altitude portion, where isoprene is absent. Taken together, these results suggest minor discrepancies in the distribution of isoprene oxidation products in RACM2. The utility of direct rate analysis afforded by box models cannot be overstated, especially for chemical species with multiple sources and sinks. A true mechanism evaluation also requires comparison to measurements where possible. The SENEX dataset lacks HOx observations, but it does include a wide range of isoprene oxidation products. Work is ongoing to evaluate isoprene chemistry within these mechanisms using observations of HCHO and other species from the full SENEX mission (Marvin et al., 2016).