Like any box model, ARCA does not consider spatial variation and the related processes, most importantly advection (including convection). When simulating ambient (field) processes, we must therefore assume that the conditions are spatially homogeneous. The transport equation, describing the local change in scalar variable S in terms of its total derivative and advection in wind field V, then becomes 1∂S∂t=dSdt-V∇S≈dSdt, which is an acceptable approximation when |dS/dt|≫|V∇S|, as is the case with fast chemical reactions but not necessarily for slow processes like aerosol growth and coagulation losses. This alone will produce inevitable deviation between modelled (following dS/dt) and locally measured (following ∂S/∂t) time series.

The particles in the discrete aerosol size distribution are assumed to be spherical, liquid-phase droplets with constant density (ORGANIC_DENSITY). Charges are omitted and all particles are treated as electrically neutral (ion-mediated nucleation is considered in the ACDC module, which calculated the stable cluster formation rate). Liquid-phase organic chemistry in the particles, for example polymerization and the consequential effects this has on the thermodynamics (sometimes called ageing), is not considered in the model. In the present model version particles of all sizes – even above activation diameter – are completely void of water, and the dissolution of inorganic compounds is therefore ignored. Some of these restrictions will be addressed in the near-future updates; see Sect. 7, which also discusses some of the possible implications of the currently missing particle-phase chemistry.

The ACDC nucleation module is more flexible than the aerosol module and – given the proper input – would be capable of simulating also hydrated clusters, but presently neither of the included cluster chemistry systems contain hydrated clusters.

The main processes modelled in ARCA box are (in the order of execution) (1) gas-phase chemistry, (2) formation of molecular clusters, (3) reversible vapour wall losses, (4) gas-particle partitioning (condensation and evaporation, using the APC scheme), (5) coagulation of particles and (6) wall loss of particles (Fig. 1). The processes – which can be switched on and off in any combination – are executed in a series in which the next process relies upon values which were calculated in the previous process. Compared to a method where all changes within a time step are solved as one coupled system, this has the advantage that adding more processes (or skipping them) is straightforward as they can simply be added to the main loop as a subroutine or module and solved in any suitable way. On the other hand, the forward integration requires that the time step is kept small enough to justify the linearization of a non-linear system. The default time step (10 s) is usually a good compromise between stability and computational efficiency, but the model also includes a time step optimization algorithm (described in Sect. 2.3).

Programmatically the model consists of two main parts: the numerical model (in Fortran), which should be compiled on the computer where it is executed, and the graphical user interface GUI (in Python). Both software environments are freely available for Windows, Mac and Linux, and the model has been successfully installed and used on all three platforms. The numerical module is configured and initialized with a setting file, called hereafter INITFILE, defining all the simulation settings. Additional input includes the spectral irradiance or actinic flux, pure liquid saturation vapour pressures of low-volatility organic compounds and (optionally) the elemental composition of the condensing vapours, and (also optionally) time series of environmental variables, precursor gases, initial or background aerosols, and aerosol loss rates, if the built-in parametrization is not used.

The model can be used with a fixed time step DT (default time step is 10 s) or with multiple, dynamically changing time steps. With the latter the user defines the maximum and minimum relative change in one time step for (1) particle diameter (ddp), (2) particle number concentration in each bin (dNp) and (3) concentration of condensable vapours (dC). After exiting each module (shown in Fig. 1), the changes in 1–3 are calculated. If the module produced changes that exceed the maximum, the time step for that module is halved, and the current integration time step will start over. In contrast, when the largest change is below the tolerance minimum, the time step of that module is doubled. The modules are assigned with one of the three time steps, denoted CCH (condensation and chemistry), COA (coagulation) and DEP (losses). The processes used to control the time steps are shown in Table 1.

When time step optimization is used, a three-element vector DT_UPPER_LIMIT defines the maxima for CCH, COA and DEP, and the nominal model time is used as a minimum (by default the GUI sets DT to 1 ms). Therefore, the three time steps are defined by multiplying the nominal model time step by a factor of 2n, where n={1,2,3…}, and satisfy DT<Δt×2n≤DT_UPPER_LIMIT. Optimizing time step in this way has two effects. It helps to overcome the potential error created by decoupling of different modules that are not solved together as one dynamic equation (notably condensation to particles and chemistry) by guaranteeing that the changes in one time step are small. On the other hand, when a process is very slow, such as aerosol coagulation, the extra precision gained by a small time step is negligible; instead increasing the time step can shorten the computational time significantly. The effect on the execution time of the simulation depends on the tolerances and the conditions of the simulation. With loose tolerances (5 %–10 %) the simulation time is usually shortened, while tight tolerances (0.2 %–3 %) will increase runtime markedly. The time step optimization should first and foremost be seen as a safeguard against diverging too far from the true solution of the integration.

The chemistry code of ARCA is based on the KPP (Kinetic PreProcessor, https://people.cs.vt.edu/asandu/Software/Kpp, last access: 23 September 2022; Damian et al., 2002; Sandu et al., 2003; Daescu et al., 2003), and any reaction set which complies with the KPP format can be used to create ARCA's chemistry modules. An often used source for atmospheric chemistry schemes is the MCM v3.3.1 (Master Chemical Mechanism version 3.3.1, http://mcm.york.ac.uk/MCMv3.3.1, last access: 23 September 2022) (Jenkin et al., 1997, 2015; Saunders et al., 2003), which provides the gas-phase chemical reactions and rates of the degradation of specific organic compounds in the atmosphere, as well as detailed inorganic chemistry and photochemistry. The full scheme – or a subset – can be downloaded from MCM website in KPP format. Optionally, the user might have additional chemistry schemes, which need to be combined with the MCM scheme, such as the PRAM scheme (Peroxy Radical Autoxidation Mechanism; Roldin et al., 2019) which describes the production of highly oxygenated molecules (HOMs) from monoterpenes and is included in the ARCA distribution. ARCA's GUI has a tool (“create chemistry scheme”) which combines different schemes, removes duplicate compounds, and reactions and creates a valid single KPP definition file, used for producing a Fortran module with KPP. A modified source code of KPP v2.2.3, accommodated for very large schemes, is provided with ARCA. The generated code will then be part of ARCA and is available for use after compilation. Switching between different chemistry schemes can later be done in the GUI with a drop-down menu.

The main use of ARCA, besides simulating chemical reactions in the gas phase, is to compute the evolution of a population of aerosol particles experiencing dynamical processes such as coagulation, deposition and phase transition. There are many ways to formally approach this task, discussed, for example, by Whitby and McMurry (1997). In the atmosphere, the number of condensing species, different particle sizes and compositions is unlimited, and the practical mathematical descriptions of the PSD therefore require simplifying assumptions. The aerosol dynamics models are often characterized by their representation of the PSD. Typical representation types are the discrete, the spline, the sectional, the modal and the monodisperse representation.

In the discrete representation, particles have a discrete size and composition. That is, one size section includes exactly one discrete particle composition, given by the exact numbers of molecules of different compounds in the particle. This approach must be used when explicitly modelling initial cluster formation but gets increasingly complex and numerically heavy when more “building blocks” are added, such as chemical compounds or particle sizes. ARCA's nucleation module consists of the ACDC model which uses discrete representation.

Sectional models decrease complexity of the system by grouping parameters, and typically the particle diameter range (and equivalently volume, mass and surface) is divided into a limited number of intervals or size bins. Particles in each bin have the same properties. This is a common approach in atmospheric modelling; however, its accuracy depends on the number of bins used and on the magnitude of change applied within one integration time step Δt. While large changes within Δt lead to a deviation from the analytical solution, small changes cause numerical diffusion especially when simulating condensational growth (Gelbard and Seinfeld, 1980).

ARCA allows to choose between two sectional representations, the fully stationary (FS; Gelbard and Seinfeld, 1980) method and the fixed-grid moving average method (MA, also called “moving centre sectional”; Jacobson, 1997a). The future roadmap includes a hybrid method, discussed in Sect. 7. The current representation methods are graphically summarized in Fig. 4.

The FS method is very robust during computation but does not treat growth continuously, and therefore it suffers from numerical diffusion (Jacobson, 1997a). This is the result of the redistribution, in which particles are assigned to bins below and above the actual size the particles have grown (or shrank) to be, thereby introducing particles that are larger (or smaller) than those the condensation or evaporation produces. In time this will lead to spreading of the size distribution, much like a diffusive process. The MA method strongly reduces numerical diffusion as the particle diameter within the size grid can continuously change, and particles are not distributed between bins. The main drawback of the MA method is the appearance of numerical artefacts, referred to as “pits” and “peaks”, affecting the analysis of the results. However, they can be removed during data analysis by remapping the data on a new size grid as described by Mohs and Bowman (2011). Both PSD methods used conserve mass and total particle number.

The choice of the PSD representation does not affect the calculations in the aerosol dynamics module as they are separated from each other. This means that the different methods to represent PSDs can be changed or added without interfering with the aerosol dynamics code. Aerosol-related parameters required to solve the dynamics are provided by accessor functions (getters) and work for any PSD representation. Further, changes to the PSD by the dynamic processes are calculated in the aerosol dynamics module but applied in the PSD module. This allows further development of the scientific and computational aspects independently.

Formation of new particles from vapours by clustering of gas-phase molecules, often referred to as aerosol nucleation, is described by simulation of molecular cluster population dynamics with quantum chemistry input for cluster evaporation rates. This yields the formation rate of new particles per unit volume and unit time.

In addition to the explicit cluster dynamics simulation, simplified formation rate parametrization can be used. Currently, a parametrization for new particle formation from H2SO4 and representative organic components is available. This option approximates the formation rate as a function of H2SO4 and user-defined set of organic compound concentrations. The choice of what organic compounds (or proxies for them) to include in the set is not unambiguous and is dependent on the active chemistry scheme and assumptions made by the user. Still, such parametrizations are commonly used to characterize empirical observations of particle formation (e.g. Paasonen et al., 2010). While they do not correspond to an explicit time-dependent formation rate and may not include all independent ambient parameters which could affect the formation rate, they are useful for assessing the magnitude of particle formation through the given chemistry.

To complement the formation rates and the parametrization, the model has also a time-dependent input variable NUC_RATE_IN. When multiple particle formation rates are calculated, either by different ACDC systems, additional parametrizations or NUC_RATE_IN, the total formation rate – used in the aerosol module – is the sum of all processes. The output files contain the total formation rate and separately those from the ACDC systems. Furthermore, if applicable, the formation rates of electrically neutral and positively and negatively charged particles are also saved. It must be emphasized that the charging states refer solely to the charges of the outgrowing particles in ACDC, not to the formation mechanisms of the particles. For instance, newly formed neutral particles may originate – and often do originate (Olenius et al., 2013) – from ion-mediated processes, in which small ions recombine, and the product grows further as a neutral cluster.

Formation and evolution of either natural or anthropogenic aerosols are dependent on gas-to-particle-phase transition via nucleation, condensation and evaporation (Tsang and Brock, 1982; Wagner, 1982) and further on coagulation (von Smoluchowski, 1918; Fuchs, 1964). In ARCA, the condensational growth of particles due to organic vapours and sulfuric acid is defined by their gas- and particle-phase concentrations and pure liquid saturation vapour pressures psat (sulfuric acid is treated as non-evaporating vapour with psat=0). ARCA employs the mass-conserving Analytical Predictor of Condensation (APC) scheme (Jacobson, 1997a, 2002), describing the condensational transfer of a gas-phase compound q onto particles in size bin i, as the change in particle-phase composition cq,i, in a time interval Δt: 4dcq,i,tdt=kq,i,t-Δt(Cq,t-Sq,i,t-Δt′Cq,eq,t-Δt), where Cq,t is the gas-phase concentration of compound q at time t, Sc,i,t-Δt′ is the equilibrium saturation ratio of the condensing gas, Cq,eq,t-Δt is the pure compound saturation vapour concentration over a flat surface, and kq,i,t-Δt is the mass transfer rate between the gas phase and all particles of size i (Jacobson, 1997a). The mass transfer rate kq,i,t=ni2πdiDeff,q,i [s-1], where ni is the number concentration of particles in size bin i, di is the diameter of the particle in size bin i, and Deff,q,i is the diffusion coefficient of compound q with particles in bin i (Jacobson, 1997b). The equilibrium saturation ratio is calculated using the Köhler equation, which combines both the Kelvin and solute effect. The Kelvin effect accounts for the changes in saturation vapour pressure over the particle due to surface curvature, with small particles having larger saturation vapour pressures. The solute effect, or Raoult's law, describes the change in saturation vapour pressures for an ideal solution with a mixture of compounds in the particle droplet. Overall, the equilibrium saturation ratio for a compound is obtained by multiplying the solute effect, expressed as the molar fraction of the compound and the Kelvin term: 5Sq,i,t′=xq,iexp⁡4σq,pmqRgdiTtρq,p, where xq,i is the organic molar fraction of compound q in a particle of bin i, σq,p is the pure liquid surface tension, mq is the molar mass of the compound, Rg is the universal gas constant, Tt is the temperature at time t, ρq,p is the liquid density of the pure compound q, and di is the diameter of particle in bin i.

The forward Euler method is used to integrate Eq. (4) over incremental time steps Δt, giving the change in particle-phase concentrations Δcq,i,t+Δt. The non-iterative solution to Eq. (4) can be written as 6cq,i,t=cc,i,t-Δt+Δtkc,i,t-Δt(Cq,t-Sq,i,t-Δt′Cq,s,t-Δt).

Equation (6) relies on final gas concentrations Cq,t, which are constrained by the mass balance equation 7Cq,t+∑i=1Nbinscq,i,t=Cq,t-Δt+∑i=1Nbinscq,i,t-Δt, where Nbins is the number of particle size bins. Combining Eq. (6) with the mass balance Eq. (7), the change in mass composition is calculated, which is then passed to the particle redistribution module. The final particle composition cq,i,t at each time step is constrained between max⁡(0,cq,i,t) to prevent evaporation from exceeding the total mass existing in each particle size bin (Jacobson, 1997b).

The most crucial factor governing the condensational growth in the APC scheme is the compound-specific pure liquid saturation vapour pressure psat. The structures of all compounds originating from MCM are available as Simplified Molecular Input Line Entry Specification (SMILES) codes, and ARCA includes a tool that can be used to extract the temperature-dependent psat information using the methods in the UManSysProp (http://umansysprop.seaes.manchester.ac.uk, last access: 23 September 2022), an online facility for calculating the properties of individual organic molecules, currently hosted at the University of Manchester. ARCA's tool converts the data acquired from UManSysProp to A and B parameters of the Antoine equation: log⁡10(Psat)=A-B/T, where psat is in atmospheres [atm], and T is the temperature [K].

There are often discrepancies that are orders of magnitudes (ranging from 10-13 to 10-5 atm) in the estimated pure liquid saturation vapour pressures of species when using different methods (Valorso et al., 2011). Therefore, ARCA includes two different files for saturation vapour pressures: one obtained using the methods described in Nannoolal et al. (2008; NANNOOLAL) and another using the EVAPORATION (Compernolle et al., 2011). The files include only those compounds whose psat≤10-6 atm (at 293.15 K), as more volatile compounds have a negligible contribution in particle growth. In both files, the saturation vapour pressures for HOMs originating from PRAM are calculated using the group contribution method SIMPOL (Pankow and Asher, 2008). Kurtén et al. (2016) have shown that NANNOOLAL produces low estimates of saturation vapour pressure for multifunctional compounds due to the absence of hydro-peroxide or peroxy-acid group parametrizations. SIMPOL, on the other hand, has been shown to be in better agreement with pure-liquid vapour pressures of multifunctional compounds calculated using COSMO-RS (Conductor-like Screening Model for Real Solvents) (Eckert and Klamt, 2002; Kurtén et al., 2016). The EVAPORATION includes a limited number of peroxides and peroxy acids (Kurtén et al., 2016) and is shown to produce the most accurate estimation of psat for all compounds for which EVAPORATION is applicable (O'Meara et al., 2014). The user can always provide their own pure liquid saturation vapour pressure data (using the same file formatting: compound_name, A, B). The GUI also contains a tool with which the NANNOOLAL and EVAPORATION data can be filtered with some other threshold than 10-6 atm.

Coagulation occurs when two particles collide and coalesce or form agglomerates, and it results in the increase in mean particle size and decrease in number concentration in the total particle distribution, while total mass is unaffected. As ARCA is primarily intended to be used within the submicron size range, the only coagulation process considered is the Brownian (thermal) coagulation, caused by the thermally induced random motion of particles. Models of Brownian coagulation have existed for over a hundred years, starting from the work by von Smoluchowski (1918). The coagulation equation (Seinfeld and Pandis, 2016) is 8∂Ni(t)∂t=12∑j=1i-1Kj,i-jNjNi-j-Ni∑j=1∞Ki,jNj,i≥2, where Ki,j is the coagulation coefficient, or coagulation kernel, between particles of size i and j, with number concentration N. Coagulation coefficient K depends on the size of the particles and increases with the particle size difference. The derivation of coagulation coefficient is different in the free molecular, transition and continuous regimes, and the commonly used method to account for this is the Fuchs form of the Brownian coagulation coefficient (Fuchs, 1964; Seinfeld and Pandis, 2016) which also accounts for the coagulation efficiency, or sticking coefficient, which is the fraction of collisions that lead to coagulation, αc (in ARCA the default ALPHA_COA=1). In general coagulation coefficients contain uncertainties and can be affected by factors which are not considered in the model, such as particle shape, hardness and electric forces (whether induced or by net charge). The thermal speed of nano-sized particles is in the order of tens of metres per second, and the probability of successful coagulation could differ substantially from 1.

Other coagulation processes, such as gravitational, turbulent or shear coagulation, are not considered in ARCA. This simplification can be justified for submicron sized particles, which are 2–3 orders of magnitudes slower compared to Brownian coagulation (Seinfeld and Pandis, 2016). If an estimation of the effect of these additional coagulation pathways is needed, they could be considered as additional loss terms and handled in the loss module.

In chamber experiments, losses of gases and particles to the chamber walls have a large influence on the outcome – the same is true for simulations. In ambient conditions losses are more complex and harder to measure due to advection, vertical mixing and different deposition processes. For simulations in confined spaces such as in a reaction chamber, the losses can be parameterized to some extent. ARCA considers losses of gas-phase compounds and particles in separate steps, as shown in Fig. 1. The compounds considered in the vapour wall loss module are the same set of organic compounds that are condensing on the particles. The wall loss is based on the theory proposed by McMurry and Grosjean (1985) and is a reversible process characterized by two reaction rates, kgas→wall and kwall→gas: 9dCq,gdt=-kgas→wallCq,g+kwall→gasCq,w,dCq,wdt=kgas→wallCq,g-kwall→gasCq,w, where Cq,g and Cq,w are the total concentrations of compound q in gas phase and wall, respectively. ARCA uses Fortran DVODE to solve Eq. (9) for each compound at each time step. Rate constant kgas→wall is derived from kinetic gas theory assuming a well-stirred chamber and is limited either by diffusion near the wall or uptake by the wall itself (McMurry and Grosjean, 1985): 10kgas→wall,q=AchVchαwνq‾4+παwνq‾2(keDq)-1, where Ach and Vch are the area and volume of the chamber, αw the accommodation coefficient, νq‾ and Dq the average thermal speed and diffusivity of molecule of compound q, respectively, and ke the eddy diffusion coefficient. αw (ALPHAWALL) is a property of the chamber wall, whereas ke (EDDYK) is a description of the turbulent conditions in the chamber. In general, we should assume that αw is different for each compound; however, these are generally not known, and a constant value of 10-5 is used as a first estimate, following, for example, Matsunaga and Ziemann (2010) and Zhang et al. (2014). Similar to surface tension data, individual αw (or correction factors to constant ALPHAWALL if set to negative) can optionally be set in the file, which defines the pure liquid saturation vapour pressure data. The rate kwall→gas is derived from a steady-state equilibrium where dCq,g/dt=dCq,w/dt=0 and Cq,g=Cq,sat; then 11kwall→gas=kgas→wallCq,satCq,w,eqv, where Cw,eqv,q is the equivalent mass concentration on the wall (Pankow, 1994; Matsunaga and Ziemann, 2010). It is assumed that the activity of compound q is always 1, rendering Cw,eqv,q to a constant Cw,eqv (CW_EQV). The value of Cw,eqv is not known, but the sensitivity to the loss of low-volatility vapours is small, above values of ∼1 µmolm-3 (Zhang et al., 2014). The default Cw,eqv=40 µmolm-3 corresponds to 10 mgm-3 for an organic molecule with a mass of 250 gmol-1.

McMurry and Grosjean (1985) discussed the effect of αw. In the limit of very small αw, Eq. (10) can be reduced to kgas→wall,q=(A/V)(αwν‾/4), and the uptake of gases is then limited mostly by surface reactions. With increasing αw, the uptake becomes diffusion-limited, finally reducing to kgas→wall,q=(2A/πV)keD, the separating value for αw which divides the two modes of uptake being at αw=(8/π)(keD/ν‾).

Aerosol losses are considered as irreversible deposition, and the first order loss rates [s-1] can either be a constant value or read from a file as (time- and) size-resolved values (which will be linearly interpolated for model times and bin diameters). If the losses are not known, they can also be approximated using parametrization from Lai and Nazaroff (2000), which considers the different deposition velocities of upwards, downwards and vertical surfaces. The necessary input is the floor area, height and the friction velocity of the chamber (CHAMBER_FLOOR_AREA, CHAMBER_HEIGHT and USTAR, respectively). The last is used to characterize the near-surface turbulent flow and can be estimated from the airflow velocity in the chamber with the Clauser plot method (Bruun, 1995) or treated as a fitting parameter. Figure 5 shows the calculated loss rates in a 10 and 30 m3 chamber (heights 2 and 3 m, respectively) with three different settings for friction velocity. Whichever way is used to derive the loss rate kdep,i, the number of particles lost from bin i, ΔNi,Δt, in time step Δt are calculated by 12ΔNi,Δt=Ni,t1-exp⁡(kdep,iΔt).

The model saves the mass composition of particles lost to walls (in kgm-3) as a cumulative sum. Since the vapour wall losses are reversible, the model saves the mass flux to and from the walls (in kgm-3s-1, positive value indicates gas to wall flux), calculated as an average over the time interval for saving results.

ARCA saves most of the output from the simulations in three compressed NetCDF4 (network common data form) files. The time resolution of the output can be defined in model seconds (FSAVE_INTERVAL) or as number of saved instances (FSAVE_DIVISION). The files contain time series of the environmental variables and nucleation rates and the names of the used ACDC systems (General.nc), gas concentrations of the complete chemical set (Chemistry.nc), and aerosol number concentration, size, coagulation sink, particle growth (by condensation module) and loss rates, vapour concentrations in particle (size-resolved) and gas phase, and the vapour fluxes to and from the particle phase and walls (Particles.nc). All files contain basic attributes of the model configuration, such as the name of the chemistry module used, user-supplied description, name of the output directories and INITFILE, (real) date, and time of the simulation.

When the model is run, a copy the INITFILE which was used to initialize the model is saved (InitBackup.txt). This file can be loaded in the GUI or used as such to repeat the simulation, provided that other input files are the same. A time series of particle number concentrations in normalized ΔN/Δ(log⁡10(dp)) and linear scale, as well as a list of condensing vapours, is provided for convenience. If the model was run from the GUI, the screen output of the numerical model is also saved (runReport.txt). A complete list and description of the output variables and files is shown in Table 2.

The primary principle of the GUI design has been that the numerical model is kept autonomous of the user interface. This ensures that the model can be run on as many systems as possible, even when the user has no access to a graphical OS, such as when working on a secure shell (SSH) connection to an HPC. Another aspect is that Fortran is a much more conservative language than Python, and it can be expected to work reliably as intended on each OS. While Python is cross-platform, its reliance on multiple extra packages and their rather quick updating schedule make it more susceptible to introduce unintended behaviour in the GUI. While such issues are usually fixed in the ARCA repository quite swiftly, it is highly convenient that the underlying numerical model is working independently of the GUI. The independence between the model and the GUI is ensured through the INITFILE, where the GUI reads and writes a Fortran namelist text file, which is used to initialize the numerical model.

Another design principle has been that the GUI should allow further model development; that is, it should be able to write, save and read in any custom options, even if they are not yet fully incorporated in the graphical layout. Some of these options might be later incorporated, and some may turn out to be unnecessary. This principle manifests itself in the GUI's tab “custom options”.

The third design principle has been to enable flexibility in the input to the model. All input is done via human readable text files. Not all modellers have their input data available in the same units or time resolution, and the GUI lets the user define theirs. However, this flexibility has limits, and in the end the input files are expected to follow a certain structure which is covered in detail in the manual. Also, the example files in the ModelLib directory can be used as a guide.

The last design principle is similar to what any graphical user interface typically aims to do: to collect the options of a program in meaningful groups and hierarchy, showing relevant and hiding unnecessary options, deriving information from user input such as parsing pathnames or calculating values, and providing assistance through help links or tool tips. It can be noted that while the amount of GUI options might seem intimidating, many of them are related to the way the input data are structured, and usually after the initial set up – which takes a while for the first time – the user can leave most options as they are and concentrate on testing further with only a few key options.

To give an overview of the GUI, Figs. 6–8 show selected screenshots of the GUI window. For in-depth instructions and descriptions, the user is directed to the online manual, which contains an instructional video and transcript of setting up a simulation with the provided example files. To keep this work concise, here we give a general overview of the key points in setting up a simulation. As an example, we have chosen the case which produces Fig. 11, and whose complete input is included in the directory ModelLib/Examples/APINENE_OXY. Figure 6a shows the tab “general options”, which contains many of the basic options for the simulation: naming of output, paths to input and output files, model time step, and toggles for the main modules. Based on the choices in the “modules in use”, other tabs will be enabled or disabled, and the work procedure is to fill out the “forms” one tab at a time and then use “run ARCA”.

After “general options”, the most crucial set of options are in the next tab “time-dependent input” (Fig. 6b). Here the concentrations of precursors and many environmental variables are defined. The logic in this tab is that any other input than temperature and pressure are optional. Any variable which is not defined here as an input will have a constant 0 value. One picks the variables that are given as input to the model from the right-hand panel “available input variables” and moves them to the selected list of input variables. Next, there are several options how to define the values of any variable. For example, O3 could come from measurements, in which case it would be read in from the ENV file from the column number defined in “column/link”, it could be a constant, in which case it would be sufficient to “shift” the default value 0 by the constant amount, or we might want to multiply the measured values by a constant “multi”. Another option would be to link the concentration to some other variable, and then one would use that variable name in “column/link”. Finally, there is a way to use parametric input in the next tab “parametric input”, where a set of sliders can be used to create a smooth time series for any given input variable. This part of setting up the model is usually somewhat time-consuming, but once properly done, the user can easily perform sensitivity tests by using the “shift” and “multi” options of any variable. Furthermore, the tool “variations” can be used for sensitivity tests, which creates a batch of simulations in which any given set of variables are varied within given ranges, containing all combinations of the different input settings.

Figure 7a shows the options related to aerosol module, such as size range and resolution of the PSD grid, its initialization with either measurements from a file or using (multi-)modal lognormal distribution (as is done in this case), and duration and size range of initialization. This tab is also where the pure liquid saturation vapour pressure properties are defined in the “vapour file” and optional “vapour elemental composition” file. In our example case, a single mode log-normal particle size distribution was used to initialize the particles in the simulation. The (multi-)modal PSD is defined by total particle number, mode diameter, standard deviation and relative contribution to the total particle number concentration (PN). The GUI plots the resulting mode in real-time and calculates total particle mass (PM) and particle area, as these are sometimes reported and can be used to fine-tune some unknown modal parameter such as the mode width.

Figure 7b shows an example of the model output during the runtime, when it is used from the GUI. The preferred way of setting up the model the first time is to start the model from the tab “run ARCA” by pressing “run model with current settings” and dealing with the eventual error messages, which might appear due to misconfiguration. If the model enters the main loop (after printing “starting main loop”), it is advisable to press “force stop” and read the initial report of the model that is printed in the “monitor” window. If there are no warning messages, and the reported unit conversions and other reported behaviour corresponds to the intent of the user, the simulation can be performed in full.

Figure 8 shows examples of the output plotting tools such as surface plots (panel a) and particle mass and size distribution plots (panel b). A useful tool is the Live update option, which shows the evolving particle size distribution surface plot during the simulation.

For any given cluster system, the formation rates in ACDC depend largely on the evaporation rates of the clusters, generally calculated from the input Gibbs free energies. Figure 9 shows formation rates calculated with the four ACDC simulation systems: two for H2SO4–NH3 and two for H2SO4–DMA. The systems calculated with the RICC2 (RICC2/aug-cc-pV(T+d)Z//B3LYP/CBSB7) method are described in Olenius et al. (2013) and can be found in the ACDC repository (https://github.com/tolenius/ACDC, last access: 23 September 2022). The DLPNO level NH3 system (DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-31++G**) was used in Besel et al. (2020), whereas the DLPNO DMA system was used in Myllys et al. (2019). Figure 9a shows the significance of ion-mediated clustering in the H2SO4–NH3 system, as is apparent when comparing the total formation rates with and without the presence of ions. It also underlines the already mentioned notion that the charge of the outgrowing clusters does not necessarily correspond to their pathway inside the system. The H2SO4–DMA cluster formation (Fig. 9b) shows weaker sensitivity to the presence of ions.

The calculations of the Brownian coagulation module were verified in two parts. Figure 10a shows the size-dependent coagulation coefficients calculated by ARCA (for comparison, see Fig. 13.5 in Seinfeld and Pandis, 2016), whereas Fig. 10b compares the evolution of a particle size distribution with an analytical solution to the Brownian coagulation of a polydisperse particle volume distribution. The solution applies the constant, size-independent coagulation coefficient 10-9 cm-3s-1 (defined by the initial concentration N0=106 cm-3 and characteristic time τc=2000 s), and for this test ARCA's calculated coefficients were replaced with the same constant coagulation coefficient (for comparison, see Fig. 13.6 in Seinfeld and Pandis, 2016). Figure 10 shows that on one hand the coagulation kernel is calculated in the same way as the source but also that the coagulation losses are correctly applied, and therefore the temporal evolution of the discrete particle size distribution in ARCA is identical to an analytical solution of the same initial size distribution.

We simulated α-pinene oxidation in a high-ozone and low-OH chamber environment, similar as in experiment 13 in Pathak et al. (2007) (Fig. 11). The 10 m3 Teflon bag chamber was initially filled with seed particles, α-pinene and 2-butanol as OH scavenger. Then O3 was introduced to the chamber. The reported mean particle loss rate (0.3 h-1) was expanded to size- and time-dependent profiles using Pierce et al. (2008), who measured the losses in the same chamber in more detail. They report an initially higher rate of loss in all their experiments and attribute this to the growth of the particles (leading to slower average loss rate) and to the enhanced loss rate of initially charged seed particles. Since ARCA in its current form does not consider charge effects, we chose to use the reported loss rates with higher initial rate. It means that the simulation is not showing the effect of the loss rate calculated by the particle loss module, but it does still verify that the rates are properly applied – given the good agreement in total particle mass time series. The simulation used moderate wall loss of condensing vapours (ALPHAWALL=5×10-5, CW_EQV=40 µmm-3 and EDDYK=0.05 s-1). The final secondary organic aerosol (SOA) mass yield of 0.169 (final SOA mass/initial α-pinene mass) calculated by ARCA agrees well with the reported 0.17. Without evaporation from the particles, invoked by the accumulation of vapours to walls and the consequential supersaturation decrease, the calculated yield is 0.176. The final concentration of vapours deposited on the walls amounted to 13.4 µgm-3. In the chemistry scheme built for this test, ozone concentration was set to the target (250 ppb) at time 1105 s and was then allowed to evolve according to the chemical reactions. Without chemical wall loss the simulated yield is 0.286, overshooting the reported yield by a factor of 1.7. The pure liquid saturation vapour pressures used were derived using the EVAPORATION method. The chemistry was acquired from MCM and amended with the PRAM, and psat data were downloaded from UManSysProp (http://umansysprop.seaes.manchester.ac.uk, Sect. 3.5), using the tools in ARCA box.

The ARCA distribution contains an example case which produces a similar simulation to what was used to produce Fig. 11. Here the initial time without ozone is omitted, and the simulation starts immediately with 250 ppb concentration. To accommodate for the initial particle losses, the initial particle number concentration was set to 4537 cm-3. This simplification makes configuring the model much more straightforward and produces the same result apart from the shift in time when compared with the experiment data.

We also performed sensitivity runs where we tested the vapour wall parameters Cw and αw. Changing Cw an order of magnitude lower and higher (to 4 and 400 µmm-3) changed the resulting yield to 0.179 and 0.166, and final total vapour mass on the wall was 7.16 and 16.46 µgm-3, respectively. For reasons discussed in Sect. 3.7 about the limit of very small αw, we saw no practical difference in the yield or vapour mass lost to walls after αw>10-4, where the uptake apparently has become diffusion-limited. The selected default value of αw (5×10-5) can be considered to be close to the value where the surface reactions start playing a role in the uptake.

ARCA box is licensed under GPL 3.0, and the licensing statements (also those from auxiliary software) are included in the source code. The source code includes software that is not written by authors of ARCA, namely the Fortran DVODE solver (“in the public domain”, or IPD), ACDC (GPL 3) and KPP, which is not strictly necessary for ARCA but provided for convenience (GPL 3), as the original KPP is not able to compile very large chemistry schemes or long variable names.

ARCA's numerical model is written in Fortran and the user interface in Python 3. These environments must be installed and properly working on the computer. Also, since the output data are mainly saved in NetCDF 4 files, this software – along with its Fortran and Python libraries – must be installed prior to compilation and use. ARCA box has been developed on the Linux platform, but due to the cross-platform nature of Python and the availability of Gnu Fortran for all three major OSs, the model has successfully been installed and used on all of them (on Windows GFortran is used through Cygwin and on MacOS through Xcode). The model has not been tested with Intel Fortran, but as it is usually compatible with GFortran, we expect no major issues. The ARCA online manual has step-by-step instructions and videos for the installation of the prerequisite environments, as well as the model itself. It also contains solutions to installation problems which have been reported to us. After the necessary environments are working, installation and compiling the model itself are straightforward with the included Python installer script. The script will install the necessary Python packages (most importantly PyQt5, PyQtGraph, NumPy, Matplotlib and netCDF4) and compile the model.