A Lagrangian convective transport scheme including a simulation of the time air parcels spend in updrafts

We present a Lagrangian convective transport scheme developed for Chemistry and Transport Models and ensemble trajectory simulations. Similar to existing schemes in other Lagrangian models, it is based on a statistical approach of calculating parcel displacements by convection. These schemes redistribute air parcels within a fixed time step by calculating probabilities for entrainment and the altitude of detrainment. Our scheme extends this approach by modelling vertical updraft velocities and the time that an air parcel spends inside the convective event, which is important for simulating the tropospheric 5 chemistry of short-lived species, e.g. it determines the time available for heterogeneous processes on the surface of cloud droplets. Two different schemes for determining the vertical updraft velocities are introduced, which are based on constant or random convective area fraction profiles, respectively. SO2 is used as an example to show that there is a significant effect on species mixing ratios when modelling the time spent in convective updrafts compared to a nearly instantaneous redistribution of air parcels. The scheme is driven by convective mass fluxes and detrainment rates that originate from an external convective 10 parameterization, which can be obtained from meteorological analysis data or General Circulation Models. Validation runs driven by ECMWF ERA Interim reanalysis data are performed with the scheme implemented into the ATLAS Chemistry and Transport Model. These include long-term global trajectory simulations of Radon-222 that are compared to measurements, and runs testing mass conservation and the reproduction of the convective mass fluxes and detrainment rates of ERA Interim. Simulated vertical updraft velocities are validated by wind profiler measurements in Darwin. 15


Introduction
The parameterization of sub-grid scale cumulus convection and the associated vertical transport is not only a key process in General Circulation Models (e.g. Arakawa, 2004), but the correct simulation of convective transport is also important for the modelling of tracers in Chemistry and Transport Models, and the treatment of convection is a large source of uncertainty for the simulation of species in the troposphere (e.g. Mahowald et al., 1995;Hoyle et al., 2011;Feng et al., 2011).
We present a Lagrangian convective transport scheme developed for Chemistry and Transport Models and ensemble trajectory simulations. Our convective transport scheme is based on a statistical approach similar to the schemes in other Lagrangian models (e.g. Collins et al., 2002;Forster et al., 2007;Rossi et al., 2016). These schemes redistribute air parcels vertically within 5 a fixed time step to simulate the effect of convection and are driven by convective mass fluxes and detrainment rates derived from a physical parameterization of convection.
However, these schemes do not take into account the different residence times of air parcels inside the convective cloud.
The amount of time spent inside the cloud is important for calculations of the tropospheric chemistry of short-lived species.
The concentrations of these species in the upper troposphere may crucially depend on the transport time of an air parcel from 10 the boundary layer to the upper troposphere (e.g. Hoyle et al., 2011). Therefore, we extend the approach of earlier schemes by simulating the time air parcels spend inside a convective cloud. An example for a species for which that is relevant is the short-lived species SO 2 , which is depleted by a range of fast heterogenous reactions inside clouds and by a gas-phase reaction with OH (e.g. Berglen et al., 2004;Tsai et al., 2010). We perform runs with an artificial tracer that is designed to imitate the most important characteristics of SO 2 chemistry to show that there is a significant effect on tracer mixing ratios when using 15 our scheme compared to a scheme with a nearly instantaneous redistribution.
The scheme is implemented into the ATLAS Chemistry and Transport Model (e.g. Wohltmann and Rex, 2009) and runs driven by ECMWF ERA Interim reanalysis data (Dee et al., 2011) are performed. Section 2 and Section 3 describe the convective transport scheme and the corresponding algorithm. Section 2 describes the modelling of entrainment, upward transport, detrainment and subsidence. Section 3 describes the method to calculate vertical updraft velocities. In Section 4, the scheme 20 is validated. Mass conservation and reproduction of the mass fluxes and detrainment rates from meteorological data are tested, global trajectory based simulations of Radon-222 are compared to measurements, and simulated vertical updraft velocities are compared statistically with wind profiler measurements from Darwin, Australia. In Section 5, simulations with a SO 2 -like tracer are shown to demonstrate that using the scheme can have a significant effect on tracer mixing ratios. Section 6 contains the conclusions. 25 2 Description of the convective transport scheme 2.1 General concept First, we will present the algorithm for forward trajectories, and will introduce the necessary adaptions for backward trajectories at the end to facilitate understanding.
A statistical approach is taken, where entrainment and detrainment probabilities are calculated for each trajectory at every 30 time step. Whether a given trajectory is entrained into the cloud or detrained from the cloud is then determined by drawing random numbers. The model is driven by convective mass fluxes and detrainment rates from meteorological data or General Circulation Models and thus relies on an external convective parameterization. Since a grid box of the meteorological analysis typically contains several convective systems that only cover a small fraction of the grid box, a statistical approach is necessary.
The approach used in existing convective transport schemes is extended here by simulating the time that an air parcel spends inside the convective event. For this, vertical updraft velocities are calculated from the meteorological analysis and some additional assumptions (a detailed account is given in Section 3). Instead of calculating the probability that an entrained air Our algorithm executes the following steps for each trajectory air parcel in every trajectory time step ∆t (typically 10 minutes): 10 1. Entrainment if air parcel is not in convection and if a test for entrainment is successful (Section 2.2) 2. If the air parcel is in convection, the following two steps are repeated with a smaller convective time step ∆t c of 10 seconds until the air parcel detrains or the end of the present trajectory time step (∆t) is reached: -Upward transport by the distance given by the convective time step and the vertical updraft velocity (Section 2.3) -Detrainment if a test for detrainment is successful (Section 2.4) 15 3. Subsidence of air parcels outside of convection in the environment (Section 2.5) The trajectory time step needs to be sufficiently short for the algorithm to work (see Sections 2.2 and 2.4).
The convective mass flux M (z) at a given location, geometric altitude z and time in units of mass transported per area and per time interval is related to the entrainment rate E(z) and the detrainment rate D(z) by mass conservation 20 where E and D are given in units of mass per area, per time interval and per vertical distance. We define both E and D as positive numbers.
In the meteorological data, the atmosphere is divided into several model layers. Usually, the convective mass flux is given at the layer interfaces, while the detrainment rates are given as mean values per layer. Entrainment rates can be calculated from the mass fluxes and detrainment rates by Equation 1. In addition, the atmosphere is divided into grid boxes with a given 25 horizontal resolution in the meteorological analysis. In the ERA Interim meteorological analysis, M is given as the grid box mean convective updraft mass flux and D as the grid box mean updraft detrainment rate per geometric altitude. M is related to the mean convective mass flux in the convective updrafts M u (per area of updraft) by where f u is the convective area fraction, which is the fraction of the area of the grid box covered by updrafts in convective 30 clouds. We will only consider updrafts here, since updraft mass fluxes typically dominate over downdraft mass fluxes (see e.g. Figure 3 in Kumar et al., 2015). It is planned to simulate downdraft mass fluxes in a future version of the model. In the following, it is assumed that the mass associated with a trajectory is equal to the mass of the other trajectories and remains constant. This implies that for global model runs, the trajectories need to be distributed uniformly over pressure. The mass associated with the trajectory is then given by air density at the trajectory location and the volume it occupies. The mass of a trajectory air parcel in such a model is typically much larger than the mass transported in a single convective event (e.g. Collins et al., 2002). For this reason and due to the statistical nature of the approach, results will only be meaningful 5 if a sufficiently large ensemble of trajectories is examined before interpretating the results. The equations of the scheme are independent of the mass associated with the trajectory. Thus, in a global model where the trajectories fill the model domain, a larger mass associated with a trajectory parcel (i.e. a lower density of trajectories per volume) leads to a lower number of trajectories in convection at a given point in time, which balances the higher mass moved per convective event.

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For modelling the entrainment of the trajectories, we assume that the atmosphere is divided in several layers, where layer k is confined by levels k and k + 1, see Figure 1. These may be identified with the model layers of the meteorological analysis. For an air parcel located in a layer between pressures p k and p k+1 , the probability ε of it being entrained in a trajectory time step ∆t is given by 15 where g 0 is the gravitational acceleration of the Earth and E dz is the grid-box mean entrainment rate integrated over the layer (resulting in the same units as the convective mass flux). The integration has to be performed over geometric altitude, which requires a conversion between pressure and geometric altitude. The equation is derived by dividing the mass per area entrained in a layer in a time step ∆t by the mass per area of the layer. It is independent of the area covered by convection.
Whether an air parcel is entrained and takes part in convection is decided by generating a uniformly distributed random 20 number r e in the interval [0, 1] in every trajectory time step and comparing that to the calculated probability. If the random number is smaller than the entrainment probability r e < ε, the air parcel is marked as taking part in convection and is therefore not tested for being entrained as long as it stays in convection. The trajectory time step needs to be sufficiently short for the algorithm to work to avoid that ε > 1 (which would mean that the air in the layer would be ventilated several times by convection during the time step).
The time when the convective event starts can be anywhere in the time interval between t and t + ∆t. For simplicity, we 5 assume that the convective event always starts at time t. This only results in a small shift of the convective event by a few minutes at most (depending on the model time step), which will be negligible in most cases.

Upward transport
If a parcel is marked as taking part in convection, it is transported upwards for the vertical distance that it will be able to ascend according to the vertical convective updraft velocity in one intermediate convective time step ∆t c (10 seconds). Then, it will 10 be tested for detrainment (see Section 2.4). This procedure will be repeated until either the test for detrainment is successful or the end of the present trajectory time step t + ∆t is reached. The short intermediate time step is necessary to capture the steep vertical gradients in the detrainment rates and convective mass fluxes. For a strong updraft of 10 m/s, a time step of 10 s corresponds to a vertical distance of 100 m, which is usually sufficient to resolve the vertical levels of the analyses.
The vertical updraft velocity inside the convective cloud is given by where R = 287 J/kg/K is the specific gas constant of air, T is temperature and the quantities are interpolated to the position of the air parcel. The equation is derived by noting that the convective mass flux in the cloud is the product of density and the vertical updraft velocity M u = ρw u (with ρ = p/(RT ) according to the ideal gas law), and by using Equation 2. The resulting velocity is in units of geometric altitude per time. 20 Neither convective area fractions f u nor vertical updraft velocities w u are usually available from meteorological analysis data. The approach used to overcome this problem in our convection scheme is to estimate a profile of f u based on observations.
We implement two methods here. The first method uses a constant climatological convective area fraction, while the second uses a stochastic parameterization (Gottwald et al., 2016). A detailed discussion of the calculation of the vertical updraft velocities is given in Section 3. 25 The vertical geometric distance ∆z conv that the air parcel ascends in an intermediate time step is Under the assumption that the coordinate system of the trajectory model is log-pressure height Z, the distance that the parcel ascends in log-pressure height is where log-pressure height is defined as Z = −H log(p/p 0 ) and H = RT 0 /g 0 . T 0 and p 0 are the reference temperature and reference pressure of the log-pressure coordinate. Other coordinate systems will require equivalent transformations. ∆Z conv is added to the vertical position of the parcel. Longitude and latitude are left unchanged.

Detrainment
If a parcel is marked as taking part in convection and has been transported upwards, it is tested next for detrainment.

5
The probability that a parcel is detrained during an intermediate convective time step is or, equivalently where M start is the convective mass flux at the start position of the air parcel and z start is the altitude of the start position.
z start + ∆z conv is the end position of the air parcel after one intermediate time step (see Figure 2). Conversions from the coordinate system of the trajectory model to geometric altitude are necessary here. The equation is derived by noting that all the air involved in convection in the layer defined by ∆z conv (regardless whether it was entrained in that layer or coming from below) can only leave via two paths: either it can be detrained or it can leave through the upper boundary. Thus, the probability is the ratio of the amount of air that is detrained between the start and end position of the air parcel and the sum of the amount 15 of air entering either from below (M start ) or through entrainment between the start and end position. The equation assumes that air coming from below behaves the same way as air entrained. That is, there is no preferred pathway out of the layer for air coming from below or for air entrained. Next, another uniformly distributed random number r d is generated. If the random number is smaller than the detrainment probability r d < δ, the parcel leaves the convection at altitude Multiplication with r d /δ ensures that the detrainment heights are uniformly distributed in [z start , z start + ∆z conv ]. This is more realistic than assuming that the air parcel always leaves at z start + ∆z conv . This would overestimate the detrainment altitude 5 systematically, since δ is the probability that the parcel detrains somewhere between z start and z start + ∆z conv . A parcel can entrain and detrain in the same trajetory time step ∆t (but can stay longer in convection, of course).
If the parcel reaches an altitude where the convective mass flux M interpolated to the position of the parcel is zero, but still has not detrained, the parcel is forced to detrain. Due to the finite time step, the air parcel may end up at a position where M = 0, which can be interpretated as numerical overshooting. While this behaviour can be avoided by decreasing the altitude  Figure 14) and on the chemistry of short-lived species (see discussion of SO 2 -like tracer in Section 5).

Subsidence outside of convective systems 20
To conserve mass and balance the updraft, parcels in the environmental air have to subside. All parcels that are currently not in convection are moved downwards by a pressure difference of where M and f u are the convective mass flux and convective area fraction interpolated to the position of the trajectory parcel.
The factor 1/(1 − f u ) is a weight introduced to compensate for not subsiding the trajectory air parcels that are in convection, 25 but is close to unity since f u is small. The fraction of trajectories that are in convection will not necessarily correlate to f u , which is based on observations independent from the convective parameterization.

Backward trajectories
A nice property of the algorithm is that it also works for backward trajectories. Backward trajectories with convection are e.g.
useful for determining the source regions and modelling the chemical composition of air measured along a flight path or sonde Some modifications of the algorithm are necessary. First, we have to exchange the meaning of E and D in the equations (detrainment becomes entrainment backwards in time). Then, the updraft velocity w u has a negative sign. Finally, the correction for subsidence moves the air parcels upward. The "entrainment" probabilities from Equation 3 (actually "detrainment probabilities backwards in time") become The "detrainment" probabilities become In contrast to forward trajectories, the convective mass flux at the start position of the air parcel M start is at a higher altitude z start than the end position z start − ∆z conv .
If the parcel reaches either an altitude where M = 0 or goes below the surface (due to the finite time step), but still has not 10 "detrained" the parcel is forced to "detrain".

Simulation of vertical updraft velocities
Vertical updraft velocities can be calculated by Equation 4, where most quantities can be obtained from the meteorological analysis data. However, the convective area fraction f u is not available from the meteorological analysis and has to be obtained independently. 15

Constant convective area fraction
The first method is to use a constant climatological profile f u (z) of the convective area fraction. For this profile, we use C-band dual polarization (CPOL) radar measurements conducted in Darwin, Australia, and define a profile which closely follows the profile in Figure 2 of Kumar et al. (2015) (red lines using the "space approach"). The profile is representative for a 190 x 190 km 2 grid box centered over Darwin and is shown in Figure 3. As a result, the variability of the vertical velocities arises 20 mainly from the variability of M then. The choice of a tropical profile is affected by our first application cases. An obvious shortcoming of this method is that it assumes a globally constant convective area fraction, which is certainly not realistic.
Hence, we implement a second method to improve on this.

Random convective area fraction
The second method uses a stochastic parameterization of the convective area fraction conditioned on the large scale vertical 25 velocity at 500 hPa, which is described by Gottwald et al. (2016). The method is based on estimates of convective area fractions derived from CPOL radar measurements over Darwin (wet seasons 2004/2005, 2005/2006, 2006/2007 and Kwajalein, Marshall Islands (May 2008 to January 2009) averaged over 6 hours. The large-scale meteorological state, e.g. the

Limitations and possible alternatives
An alternative approach is to use a climatological profile of measured mean vertical velocities together with some method to obtain variability by scaling the profile, i.e. not to use Equation 4. However, this has the disadvantage that the shape of 10 the wind profile is always the same. Measurements of updraft velocities are available from in situ aircraft observations (e.g. LeMone and Zipser, 1980), airborne Doppler radar (e.g. Heymsfield et al., 2010) or ground-based wind profilers (e.g. May and Rajopadhyaya, 1999;Kumar et al., 2015). In combination with the given convective mass fluxes, this method of obtaining the vertical updraft velocities may lead to inferred convective area fractions greater than 1. This issue is equivalent to the issue of the unrealistic vertical updraft velocities in the method using the convective area fractions. 15 A limitation of our method to derive f u is that it does not take into account the convective mass flux at the trajectory position. It may be possible to base the convective area fractions on convective mass flux as the large scale variable. This requires measured convective mass fluxes, which can only be obtained from simultaneous measurements of convective area fractions and updraft velocities (see Kumar et al., 2015).  Tiedtke (1989), with several modifications (e.g. Bechtold et al., 2004). The trajectory model is the model that is used in the ATLAS Chemistry and Transport Model (Wohltmann and Rex, 2009), extended for the convective transport scheme.
While the quality of the used convective mass fluxes and detrainment rates will have a large impact on the results of the

Mass conservation and reproduction of convective mass fluxes and detrainment rates
For the technical verification of the algorithm, we test mass conservation and the reproduction of the archived convective mass fluxes and detrainment rates. We use a simplified and non-realistic setup here that facilitates interpretation. How well the results of our model compare with reality is an independent issue that will be discussed in Section 4.2 and is examined with a more realistic setup. We also use the more realistic setup to test mass conservation more rigorously later.

5
In the simplified setup, we start 100,000 trajectories that are uniformly distributed in pressure between 1000 hPa and 100 hPa   with pressures lower than 1000 hPa, but that some surface pressures from ERA Interim in the simulated region are higher. This causes some trajectories to end with pressures above 1000 hPa. Results for backward trajectories or the random convective area fraction profile look very similar (not shown).
In the simplified setup, a significant fraction of the trajectories will not move at all, because they are initialized in a position where the convective mass flux and entrainment rate are zero. In Figure 5, the number of these trajectories is shown in black.

5
A more rigorous test of mass conservation with a long-term simulation driven by the actual large scale wind fields is shown in the next section.

Validation of the convection scheme with Radon-222
A validation with measurement data is performed by comparing the results of long-term global trajectory simulations of Radon-222 to measurements. These results will depend on the used meteorological data.
Radon-222 is formed by the radioactive decay of uranium in rock and soils and has been widely used to validate convection models and to evaluate tracer transport (e.g. Jacob et al., 1997;Feng et al., 2011). Its popularity is due to some favorable 5 properties: It is chemically inert, is not subject to wet and dry deposition and is only removed by radioactive decay. The halflife time of 3.8 days is in the right order of magnitude to detect changes in convective transport. However, the measurement coverage of Radon is quite limited (in particular for profiles) and emissions, which can vary with region and time, are uncertain (e.g. Liu et al., 1984;Mahowald et al., 1995).  There is also no mixing of air parcels to simulate diffusion, contrary to the stratospheric version of the model (Wohltmann and Rex, 2009). Given the resolution of the model runs and the short half-life time of Radon, we believe that these simplifications are justified.  Figure 10 shows the same for December to February (7 sites, no standard deviation available).
In addition, we show comparisons to aircraft campaign measurements from coastal locations around Moffett Field (37.5 • N, 122 • E, California) in June and August 1994 in Figure 11 (Kritz et al., 1998) and to aircraft measurements from coastal regions in Eastern Canada (Nova Scotia) from the North Atlantic Regional Experiment (NARE) campaign in August 1993 in Figure 12 (Zaucker et al., 1996). Simulation results are averaged over the campaign periods and a longitude-latitude bounding 15 box encompassing all aircraft measurements.
The agreement to the measurements is reasonable, given the large uncertainties in measurements and emissions. Runs with convection agree better with the measurements than runs without convection. There is an underestimation of Radon by the simulations in the middle troposphere. This may be caused by the fact that several measurements are from coastal areas, where the Radon gradient is high and difficult to model. 20 The results for both vertical updraft velocity parameterizations are nearly identical because of the globally constant lifetime of Radon (a globally constant lifetime implies that for an air parcel in a given layer, only the time since the last contact with the boundary layer matters and not the exact path that the trajectory has taken to the layer). For the same reason, an almost instantaneous redistribution of air parcels as in Collins et al. (2002) will also lead to results very similar to the results shown for the two vertical updraft velocity parameterizations. Hence, it is not possible to give a recommendation for one of the vertical 25 updraft velocity parameterizations from the results of the Radon simulations.
For this reason, we perform runs with a SO 2 -like tracer with a varying lifetime in Section 5. Unfortunately, species like SO 2 , where different vertical updraft velocity parameterizations lead to significantly different tracer concentrations are often difficult to validate with measurements. This is due to the large uncertainties in the chemistry schemes and microphysics for these species, uncertain emissions and sparse measurement coverage.    Noconv Const CAF Random CAF Measurements Figure 12. Observed radon from aircraft measurements of the North Atlantic Regional Experiment (NARE) campaign in August 1993 (Zaucker et al., 1996)   The agreement between the measurements and the modelled values for the random convective area fraction method is quite satisfactory, when only velocities greater than 0.6 m/s are considered, giving some confidence in the method. In particular, the magnitude of the exponential decrease in the frequency distribution is met quite well. Using the random convective area fraction profile method clearly leads to higher vertical velocities on average than using the constant convective area fraction profile.
I.e., the random convective area fraction profile method shows a higher frequency of large vertical velocities than the constant convective area fraction profile method, which is in better agreement with observations. The agreement of the measurements to the modelled values from the constant convective area fraction method is worse for values of more than 5 m/s than for the 5 random convective area fraction method.
It is difficult to say what the reason for the marked disagreement between model and measurements in the small vertical updraft velocities is. The number of small values is sensitive to the method to determine convective situations in the wind profiler measurements, and may change significantly depending on the method. It is common in other publications to apply a lower threshold to the vertical updraft velocities to obtain convective profiles (e.g. LeMone and Zipser, 1980;May and 10 Rajopadhyaya, 1999;Kumar et al., 2015). For the modelled profiles, the distribution of the velocities is determined by a large number of factors and may change significantly depending on the details of implementation and the convective parameterization in the underlying meteorological analysis. E.g., the assumed convective area fraction profile and the assumptions in the Tiedtke scheme will play a large role. Hence, we don't expect more than a qualitative agreement between model and measurements. Note that the model is trained on convective area fraction data measured in Darwin and Kwajalein and compared to wind 15 profiler data measured at Darwin, while it is applied to a larger region covering a large part of the tropical Pacific here. The lack of other measurements does not allow for a completely independent model validation. Figure 14 shows the frequency distribution of the residence times of the trajectories between entrainment and detrainment simulated by the two parameterizations for the vertical updraft velocity (solid lines). It is evident that most convective events 20 have a residence time of less than 30 minutes (more than 95% for the constant convective area fraction profile). Since the number of convective events is dominated by shallow convective events, which typically only lift the air parcel a few 100 m in one trajectory time step (see Figure 4), we also show the frequency distribution for deep convection (approximated by detrainment events above 300 hPa). These will be more relevant for the upper tropospheric mixing ratio of short-lived species.

Residence time in convection
Typical residence times of deep convective events are around 1 hour for the constant convective area fraction profile. The 25 simulation with the random convective area fraction profile shows a higher number of convective events with a short residence time and correspondingly, a lower number with long residence time, compared to the simulation with constant convective area fraction profile. This is consistent with the larger simulated vertical updraft velocities for the random profile.

Simulations with a SO 2 -like tracer
To demonstrate that there is a benefit to simulate the vertical updraft velocity and the time spent in convective clouds, we 30 perform runs with an artificial tracer that is designed to imitate the most important characteristics of the short-lived species SO 2 (a detailed model of SO 2 chemistry and emissions is complex and is outside the scope of this study). SO 2 is depleted by gas-phase reaction with OH and by several fast heterogenous reactions in the liquid phase in clouds (mainly by H 2 O 2 ).
The lifetime with respect to the OH reaction is on the order of days to weeks (e.g. Rex et al., 2014), while the lifetime in the presence of clouds is on the order of hours to days (e.g. Lelieveld, 1993). Hence, we perform runs with a tracer which has a lifetime of 0.1 days when in convection and of 10 days when not in convection. Emissions are distributed uniformly over the globe. Trajectory time step is 10 minutes. 5 Four different runs are performed: a run without convection, a run with a constant convective area fraction profile, a run with random convective area fraction profiles and a run where the vertical updraft velocity is set to a constant value of 100 m/s to mimic the almost instantaneous redistribution in other Lagrangian convective transport schemes (e.g. Collins et al., 2002). The setup of the runs is identical to the Radon runs, except again that only one year is simulated. Figure 15 shows the mean simulated profiles in the tropics (30 • S-30 • N) for the four different runs. The run without 10 convection shows larger values than the other runs in the lower troposphere, since the tracer is always depleted with a long lifetime of 10 days. The runs with convection show smaller values due to the fast depletion in the convective cloud. In the upper troposphere, the run without convection shows lower values than the other runs, since the transport times to the upper troposphere are much longer in the run without convection. In the runs with convection, larger vertical updraft velocities lead to shorter residence times in the cloud, and hence, to higher values of the tracer. 15 While the difference between the run with the almost instantaneous redistribution and the runs using the convective area fraction is significant, the two schemes for the convective area fraction only show a small difference. This means that the scheme is robust with respect to the exact parameterization of the vertical updraft velocities, as long as the order of magnitude of the velocities is right.

Conclusions
We present a newly developed Lagrangian convective transport scheme for Chemistry and Transport Models and ensemble trajectory simulations. The scheme is driven by convective mass fluxes and detrainment rates from meteorological data or 5 General Circulation Models and relies on an external convective parameterization. Our scheme extends the usual approach used in Lagrangian models of statistically redistributing air parcels within a fixed time step by modelling the time that an air parcels spends inside the convective event. This is important for correctly simulating the chemistry of short-lived species in the troposphere and may be crucial for determining their mixing ratios in the upper troposphere (e.g. Hoyle et al., 2011). As an example, we show that there is a significant effect on the mixing ratios of SO 2 when using our scheme compared to a scheme 10 with a nearly instantenous redistribution of air parcels (see Figure 15).
Runs are performed with the convective transport model implemented into the ATLAS Chemistry and Transport Model (e.g. Wohltmann and Rex, 2009) and are driven by ECMWF ERA Interim reanalysis (Dee et al., 2011).
The algorithm is successfully validated by showing that the scheme is able to reproduce the convective mass fluxes and detrainment rates from the meteorological data within a few percent. Mass conservation in a global 15 year trajectory simulation 15 is also within a few percent, with no apparent trend. Two parameterizations for the vertical updraft velocities are tested and compared to wind profiler measurements conducted at Darwin, Australia. The two parameterizations use either a constant or a random convective area fraction profile. Frequency distributions of the modelled vertical velocities agree well with the measurements for the random convective area fraction method and vertical velocities larger than 0.6 m/s, but show some discrepancies for small vertical velocities or the constant convective area fraction method. However, it turns out that it is a favorable property of the scheme that the results for chemical 5 tracers are robust with respect to the exact parameterization of the vertical updraft velocities, as long as the order of magnitude of the velocities is right.
Global long-term trajectory simulations of Radon-222 driven by the ECMWF ERA Interim reananlysis and using the convective transport scheme are performed to examine how well the model compares to observations. The runs show a reasonable agreement to the measurements. It is however difficult to draw clear conclusions from the validation with these measure-10 ment data due to the large uncertainties in emissions, the limited amount of measurements and the dependence on the used meteorological data used by the convective transport scheme. Future work will include e.g. the simulation of downdrafts and improvements in the mid-latitudes. For this work, we largely concentrated on the performance in the tropics, the region of the first application cases.
So far, the scheme has been applied in the calculation of the origin and convective properties of air sampled during flights of 15 the StratoClim campaign, and has been used for transport and chemistry calculations of SO 2 to determine the contribution of SO 2 to the stratospheric sulfur burden. These application cases will be presented in separate studies.
Code and data availability. The source code is available on the AWIForge repository (https://swrepo1.awi.de/). Access to the repository is granted on request under the given correspondence address. Radon climatological profile over land for the NH mid-latitude region was obtained from Liu et al. (1984). The aircraft Radon measurements of the Moffett field and NARE data are available from the Table 1 in 20 Kritz et al. (1998) and Table 3 in Zaucker et al. (1996) respectively. Vertical wind profiler data are available upon request to Alain Protat (alain.protat@bom.gov.au).
Author contributions. IW and RL developed and validated the convection model. MR initiated the model development and contributed to the discussion. GG and KP provided the stochastic model for the convective area fraction and contributed to the discussion. WF contributed to the discussion and provided the Radon data. AP provided the Darwin wind profiler data and contributed to the analysis of the vertical 25 velocity comparisons. VL provided the CPOL cloud top heights extracted over the Drawin profiler site. CW produced the dual-frequency vertical air velocity retrievals.
Competing interests. The authors declare that they have no conflict of interest.