We present a Lagrangian convective transport scheme developed for global chemistry and transport models, which considers the variable residence time that an air parcel spends in convection. This is particularly important for accurately simulating the tropospheric chemistry of short-lived species, e.g., for determining the time available for heterogeneous chemical processes on the surface of cloud droplets.

In current Lagrangian convective transport schemes air parcels are stochastically redistributed within a fixed time step according to estimated probabilities for convective entrainment as well as the altitude of detrainment. We introduce a new scheme that extends this approach by modeling the variable time that an air parcel spends in convection by estimating vertical updraft velocities. Vertical updraft velocities are obtained by combining convective mass fluxes from meteorological analysis data with a parameterization of convective area fraction profiles. We implement two different parameterizations: a parameterization using an observed constant convective area fraction profile and a parameterization that uses randomly drawn profiles to allow for variability. Our scheme is driven by convective mass fluxes and detrainment rates that originate from an external convective parameterization, which can be obtained from meteorological analysis data or from general circulation models.

We study the effect of allowing for a variable time that an air parcel spends in convection by performing simulations in which our scheme is implemented into the trajectory module of the ATLAS chemistry and transport model and is driven by the ECMWF ERA-Interim reanalysis data. In particular, we show that the redistribution of air parcels in our scheme conserves the vertical mass distribution and that the scheme is able to reproduce the convective mass fluxes and detrainment rates of ERA-Interim. We further show that the estimated vertical updraft velocities of our scheme are able to reproduce wind profiler measurements performed in Darwin, Australia, for velocities larger than

The parameterization of sub-grid-scale cumulus convection and the associated vertical transport is a key procedure in general circulation models (e.g.,

Lagrangian (trajectory-based) models have several advantages over Eulerian (grid-based) models; for example, they do not introduce artificial numerical diffusion and there is no additional computational cost for transporting more than one tracer species

We present a Lagrangian convective transport scheme developed for global chemistry and transport models. The scheme can also be used for applications such as backward trajectories starting along flight paths or sonde ascents, for which it allows for simulating the effect of convection when using a statistical ensemble of trajectories starting at every measurement location. Our convective transport scheme is based on a statistical approach similar to schemes in other Lagrangian models

These schemes therefore do not take into account the variable residence times of air parcels inside a convective cloud. The amount of time spent inside the cloud is particularly important when considering 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 the boundary layer to the upper troposphere

Therefore, we extend the approach of earlier schemes by simulating the variable residence time air parcels spend inside a convective cloud by estimating vertical updraft velocities. Vertical updraft velocities are obtained from combining convective mass fluxes from meteorological analysis data with a parameterization of convective area fraction profiles. The scheme is implemented into the trajectory module of the ATLAS chemistry and transport model

We test the scheme for the conservation of the vertical mass distribution and for reproducing the convective mass fluxes and detrainment rates of the meteorological analysis used to drive the model. Particular emphasis is given to the study of different methods of parameterizing the convective area fraction profiles needed to simulate vertical updraft velocities. All of these tests are performed with idealized trajectory simulations that ignore the large-scale wind fields to facilitate interpretation.

In addition, global long-time trajectory simulations that use the large-scale wind fields are performed. These include simulations of radon-222, which are compared to aircraft measurements, and the simulation of an artificial tracer that is designed to imitate the most important characteristics of

Radon-222 is widely used to validate convection models and to evaluate tracer transport

When considering the convective transport of an

The outline of the paper is as follows: Sects.

The source code is available on the AWIForge repository (

We first present the algorithm for forward trajectories and introduce the necessary adaptations for backward trajectories at the end to facilitate understanding.

A statistical approach is taken whereby entrainment and detrainment probabilities are calculated for each trajectory at every time step. Whether a given trajectory air parcel is entrained into a cloud or detrained from a cloud is then determined by drawing random numbers. The model is driven by convective mass fluxes and detrainment rates provided by meteorological analysis data or by general circulation models. Typical resolutions of meteorological analysis data are of the order of

We extend the approach used in existing convective transport schemes by allowing for a variable time that an air parcel spends inside the convective event. To determine this time, vertical updraft velocities are calculated by combining convective mass fluxes from meteorological analysis data with parameterizations of convective area fraction profiles (a detailed account is given in Sect.

Our algorithm executes the following steps for each trajectory air parcel in every advection time step

Entrainment if the air parcel is not in convection and if a test for entrainment is successful (Sect.

If the air parcel takes part in convection, the following two steps are repeated with a smaller intermediate convective time step

upward transport by the distance given by the convective time step

detrainment if a test for detrainment is successful (Sect.

Subsidence of air parcels outside convection in the environment (Sect.

The Lagrangian convective transport model is driven by convective mass fluxes and detrainment rates from meteorological analysis data or from general circulation models and thus relies on an external convective parameterization. The convective mass flux

In meteorological analysis 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 the mean values of the layers. Entrainment rates can be calculated from the mass fluxes and detrainment rates using Eq. (

In the following, it is assumed that every trajectory air parcel is associated with a mass equal to the mass of the other trajectory air parcels and is constant in time. While there is no natural way to assign a mass to a single trajectory air parcel, this is different in a global model wherein the model domain is filled with trajectory air parcels. One could argue that an air parcel only refers to an infinitesimally small volume and that only intensive quantities such as density are well defined for a trajectory air parcel, while extensive quantities such as mass are not well defined. However, in a global model, the volume of the model domain can be divided into smaller subvolumes that make up the complete volume. Each subvolume can be associated with a trajectory air parcel, and the air parcel mass is given as the product of the density of air and the air parcel volume. The same constant mass can be assigned to each trajectory air parcel, which implies that the associated volume is increasing with decreasing air density. Since the subvolumes of air parcels should not overlap to avoid the same air volume being counted twice, this implies that the trajectory air parcels need to be distributed uniformly over pressure (but exponentially decreasing over altitude).

This is not merely a theoretical consideration, but it becomes important when, e.g., the total mass of a chemical species is calculated or the mass flux of a chemical species through a control surface (as the tropopause).

The mass of a trajectory air parcel in such a model is typically much larger than the mass transported in a single convective event

Schematic representation of the entrainment step. All quantities are per unit area.

To model the entrainment of the trajectory air parcels we follow the approach of

Whether an air parcel is entrained and takes part in convection is decided by generating a uniformly distributed random number

The time of the entrainment event can be anywhere in the time interval between

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 in one intermediate convective time step

The vertical updraft velocity inside the convective cloud is determined by noting that the convective mass flux in the cloud is the product of density and the vertical updraft velocity

Neither convective area fractions

Once the vertical updraft velocity

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

The probability that a parcel is detrained during an intermediate convective time step

Schematic representation of the detrainment step. All quantities are per unit area.

Whether the air parcel is detrained and leaves convection is decided by generating a uniformly distributed random number

The approach for detrainment described above differs from the approach employed in previous Lagrangian convective transport schemes, since it takes into account the explicit simulation of the time that air parcels spend in convective updrafts, whereas schemes such as those employed in

If the parcel reaches an altitude at which the convective mass flux

If the air parcel detrains before reaching the end of the present advection time step

The size of the advection time step

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

Alternatively, the fraction of trajectory air parcels that are currently in convection in the model run could be used. This is, however, only possible for global runs. The mass flux of trajectories through a given surface is not necessarily balanced for non-global ensembles of trajectories. The approach would require averaging the results over a volume that is small enough to allow for variations in the fraction but large enough to contain a sufficient number of air parcels.

Another alternative would be to subside all air parcels and not only the air parcels that are currently not in convection

An attractive feature of the algorithm is that it can be readily employed for backward trajectories. Backward trajectories with convection are useful for, e.g., determining the source regions of air measured along a flight path or sonde ascent and modeling their chemical composition.

The following modifications of the algorithm are necessary. First, the meaning of

If the parcel reaches either an altitude at which

Vertical updraft velocities can be calculated by using Eq. (

The first method uses a constant climatological profile

The constant convective area profile used in the method is shown in Fig.

Constant convective area fraction profile used for calculating vertical updraft velocities.

The scanning area of the radar is comparable to typical grid sizes of meteorological analysis data.

Our scheme was originally developed for application in the tropics. Note that an application of the algorithm in the extratropics would require a different convective area fraction profile. We present simulations for the tropics as well as global long-time simulations of radon-222 in Sects.

To account for variable convective area fraction profiles as observed in measurements, we now implement a second method.

The second method uses a stochastic parameterization of the convective area fraction to obtain randomly drawn convective area fraction profiles and was introduced by

We combine the Darwin and Kwajalein data into one dataset to increase the number of measurements.

Cumulative frequency distribution of the natural logarithm of the convective area fraction from a combined Darwin–Kwajalein CPOL radar dataset as a function of the large-scale vertical velocity at 500

To derive the frequency distribution used in this study, the combined data are binned into a two-dimensional lookup table, which uses bins for the large-scale vertical velocity and bins for the natural logarithm of convective area fraction. The logarithm is used to obtain a more uniform distribution over the bins. The resulting lookup table is shown in Fig.

The large-scale vertical velocity of ERA-Interim at 500

Due to the stochastic character of the method, it is unavoidable that unrealistic vertical updraft velocities are produced from time to time. To prevent unrealistically large values, vertical velocities larger than 20

We tacitly assume here that the large-scale vertical velocities of the Darwin–Kwajalein dataset, which are used to determine the convective area fraction profile, and those of the reanalysis are comparable. It is known that differences exist for the large-scale vertical velocities of different reanalysis datasets, which in addition depend on the horizontal resolution of the reanalysis

Frequency distribution of the vertical velocities at 500

The frequency distribution of the measured convective area fractions depends on the size of the measured area from which the frequency distribution is derived. We use the full domain size of the radar of

Dependence of the standard deviation of the frequency distribution of measured convective area fractions on the domain size of the CPOL radar. Shaded areas show the standard deviation for a domain size of

Figure

A limitation of our stochastic parameterization to derive

Alternatively to our approach to estimate the vertical updraft velocity via the convective area fraction and using Eq. (

We examine the performance of our Lagrangian convective transport model by testing the conservation of the vertical mass distribution and the reproduction of the convective mass fluxes and detrainment rates of the meteorological analysis in an idealized trajectory simulation, which ignores the large-scale wind fields. Within the same idealized setup, we show that our method yields vertical updraft velocities that are consistent with observations of velocities larger than 0.6

For all of these simulations, we perform trajectory runs driven by meteorological data of the ECMWF ERA-Interim reanalysis

While the quality of the convective mass fluxes and detrainment rates will have a large impact on the results of the radon validation and the validation of the vertical updraft velocities, it is out of the scope of this study to give a validation of ERA-Interim. We refer the reader to the existing literature here

For an initial technical verification of the algorithm, we test the conservation of the vertical mass distribution and examine if our scheme appropriately reproduces the convective mass fluxes and detrainment rates of the reanalysis. We use an idealized setup here to facilitate the interpretation.

In the idealized setup, we start 100 000 trajectories that are initially uniformly distributed in pressure between 1000 and 100

Example trajectories from the run with the idealized setup for forward trajectories with large-scale wind set to zero and constant convective area profile. Open black circles mark entrainment, open red circles upward transport in convection in 10 min steps and open blue circles detrainment.

Conservation of vertical mass distribution after 20 d for forward trajectories and using a constant convective area fraction profile. Number of trajectories in 50

Figure

In the idealized setup, a significant fraction of the trajectory air parcels does not move at all because they are initialized at a position at which the convective mass flux and entrainment rate are zero. The number of these trajectories is shown in black in Fig.

Mean convective mass flux profile from ERA-Interim compared to the simulated convective mass flux profile for forward trajectories and using a constant convective area fraction profile (in a region from 180 to 240

Figure

Mean detrainment rate profile from ERA-Interim compared to the simulated detrainment rate profile for forward trajectories and constant convective area fraction profile (in a region from 180 to 240

Figure

While the mean convective mass flux and the detrainment rate profiles are insensitive to the choice of the convective area fraction profile, we see in the following section that the vertical updraft velocity profiles strongly depend on whether a constant convective area profile or a randomly drawn profile is implemented.

We validate the modeled vertical updraft velocities against wind profiler measurements. The modeled vertical updraft velocities are taken from the idealized forward trajectory runs in the tropical Pacific from Sect.

The modeled velocities are compared with measurements from a 50 and 920 MHz wind profiler pair situated in Darwin, Australia. The time resolution of the measurements is 1 min and vertical updraft velocities are obtained by the method of

Frequency distribution of vertical updraft velocities for different pressure bins from wind profiler measurements in Darwin, Australia, in 0.2

Figure

There is a large number of measurements with small vertical updraft velocities. The sensitivity of the measured distributions to these small values is quite large, and the measured distributions excluding values smaller than 0.6

It is difficult to assess the reasons for the marked disagreement between the model and measurements in the small vertical updraft velocities. 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 to apply a lower threshold to the vertical updraft velocities to define convective situations

For the modeled 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. For example, the assumed convective area fraction profile and the assumptions in the Tiedtke scheme play a large role. Hence, we do not expect more than a qualitative agreement between the model and measurements, in particular for small updraft velocities. The lower threshold of 0.1

The distribution of the vertical updraft velocities reproduces the distribution of the measurements fairly well when only velocities greater than 0.6

In the case when random convective area fraction profiles are employed our method yields a higher frequency of large vertical velocities compared to the case when the constant convective area fraction profile is implemented. The random convective area fraction profile method leads to a better agreement with observations. In particular, the two implementations differ significantly for values of the vertical updraft velocity larger than 5

The fact that the vertical updraft velocities are typically larger when a randomly drawn convective area fraction profile is used can be readily understood qualitatively:
assuming that

Replacing the simulated vertical updraft velocities by the measured
vertical updraft velocities in the model (including values smaller than

The model is trained on convective area fraction data measured in Darwin and Kwajalein and compared to wind 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

Frequency distribution of the residence times of the trajectories between entrainment and detrainment simulated by the two parameterizations for the vertical updraft velocity. The fraction of all events with a given duration is shown in 10 min bins. Solid lines show the distribution for all convective events, while dashed lines show the contribution from deep convective events (detrainment above 300

Long-time global trajectory simulations of radon-222 are compared here with aircraft observations. The results depend to a great extent on the meteorological data used. They are presented here to demonstrate that the model is able to produce reasonable results with a given meteorological analysis.

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

Global runs are performed for the time period 1 January 1989 to 31 December 2005. Trajectories are initialized at random positions (both horizontally and in pressure) between 1100 and 50

Trajectory air parcels that propagate below the surface due to the finite time step are lifted above the surface. In the uppermost layer (100 to 50

Note that the convective area fraction profile used (see Fig.

We use the same radon emissions as, e.g.,

To avoid large horizontal areas in which no trajectory air parcels receive radon emissions, a minimum boundary layer height of 500

Our approach may cause some radon that would be trapped in the boundary layer to be emitted immediately into the free troposphere and may cause some differences of the simulation to the radon measurements. However, assuming a minimum boundary layer height (or some similar measure) is unavoidable because the required number of trajectories needed for a model run that resolves the boundary layer by far exceeds currently available computational capabilities.

We revisit the issue of the conservation of the vertical mass distribution in this more realistic setup compared to the idealized setup in Sect.

Long-time conservation of the vertical mass distribution after 15 years for a run with forward trajectories using the constant convective area fraction profile and for a run without convection. We show the number of trajectory air parcels in 50

We compare the simulations to the climatological midlatitude profiles of

Observed mean radon profile obtained from measurements over land (30–60

Observed mean radon profile obtained from measurements over land (30

Furthermore, we show a comparison of our simulated radon activity to aircraft campaign measurements from coastal locations around Moffett Field (37.5

Observed radon from aircraft measurements of the Moffett Field campaign (California) in June 1994

Observed radon from aircraft measurements of the North Atlantic Regional Experiment (NARE) campaign in August 1993

The runs with convection generally show higher radon concentrations than the runs without convection in the middle and upper troposphere due to the fast transport of radon from the boundary layer to the detrainment level. A more detailed interpretation of the profiles is, however, difficult due to the large-scale horizontal averaging.

The agreement of the simulations with the measurements is reasonable given the large uncertainties in measurements and emissions. While the runs with convection agree better with the measurements than the runs without convection, there are still significant differences. For the same radon measurements, differences of a similar order of magnitude are also observed in other studies and for other convective transport models

There is an underestimation of radon by the simulations in the middle troposphere, which is most pronounced in the Moffett Field data (Fig.

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 air parcel has taken to the layer: it makes no difference if a trajectory air parcel was transported slowly upwards from the emission in the boundary layer to 10

We demonstrate that there is a benefit to explicitly simulating the vertical updraft velocity and accounting for a variable time spent in convective clouds by performing runs with an artificial tracer that is designed to imitate the most important characteristics of the short-lived species

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 for which the vertical updraft velocity is set to a constant value of 100

Mean simulated artificial

Figure

While the differences in the mixing ratios between the run involving a redistribution in a short time period and the runs employing convective area fraction profiles are significant, the two schemes using convective area fraction profiles for the computation of the vertical updraft velocities only show a small difference. Hence, for the

We will briefly discuss the implications of the differences in the simulations of short-lived species in the model runs and stress their scientific relevance in modeling the time spent in convective updrafts. A more quantitative assessment is outside the scope of this study and is planned for future studies.

Differences in

Another example for which changes in the convective transport times could be relevant is the contribution of very short-lived bromine substances (VSLSs) to the stratospheric bromine budget, which is relevant for stratospheric ozone depletion

We present a new Lagrangian convective transport scheme for chemistry and transport models. The scheme is driven by convective mass fluxes and detrainment rates that originate from an external convective parameterization, which can be obtained from meteorological analysis data or general circulation models. The novelty of our method is that we explicitly model the variable time that a trajectory air parcel spends in a convective event by estimating vertical updraft velocity profiles, in contrast to the common approach of a vertical redistribution of air parcels in a fixed time period. Vertical updraft velocities are obtained from combining convective mass fluxes from the meteorological analysis data with a parameterization of convective area fraction profiles. Convective area fractions are obtained by two different parameterizations: a parameterization using a constant convective area profile and a parameterization that uses randomly drawn profiles to allow for variability.

We performed simulations with the convective transport model implemented into the trajectory module of the ATLAS chemistry and transport model

Our scheme is able to reproduce the convective mass fluxes and detrainment rates from the meteorological analysis data within a few percent. Conservation of the vertical mass distribution in a global 15-year trajectory simulation is also within a few percent, with no apparent trend. Frequency distributions of the modeled vertical velocities agree well with wind profiler measurements conducted at Darwin, Australia, for vertical velocities larger than 0.6

Global long-time trajectory simulations of radon-222 were performed and compared to observations. The agreement with the measurements is reasonable given the large uncertainties in emissions and measurements of radon. Uncertainties in the emissions, measurements, chemistry and microphysics of short-lived species generally pose a challenge to the validation of simulations of these species, and there is a clear need to improve on this situation

An accurate simulation of the time spent in clouds 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

Future work and improvements of the method will include the simulation of downdrafts in clouds as well as extensions for applications in the midlatitudes. 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 for calculations of ammonia transport

The source code is available on the AWIForge repository (

IW and RL developed and validated the convection model. MR initiated the model development and contributed to the discussion. GAG 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 velocity comparisons. VL provided the CPOL cloud-top heights extracted over the Darwin profiler site. CW produced the dual-frequency vertical air velocity retrievals.

The authors declare that they have no conflict of interest.

This research has received funding from the European Community's Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 603557 (StratoClim). We thank the ECMWF for providing reanalysis data and Holger Deckelmann for his support in handling and obtaining the ECMWF data. Thanks go to Benjamin Segger for his work on Figs. 1 and 2.

This research has been supported by the European Commission, Seventh Framework Programme (STRATOCLIM (grant no. 603557)).The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.

This paper was edited by Patrick Jöckel and reviewed by two anonymous referees.