The global chemistry and climate model EMAC consists of the general circulation model European Centre Hamburg general circulation model version 5 (ECHAM5; ) and the Modular Earth Submodel System (MESSy; ). MESSy is a software framework to couple different submodels with a chosen base model and includes a steadily growing number of these submodels. For example, used EMAC recently to combine a global dynamic vegetation model with an atmospheric model. In this study, MESSy version 2.55 is used to link the submodel CVTRANS with ECHAM. The dynamic representation of convection is given by the Tiedtke–Nordeng convection scheme , as implemented in the CONVECT submodel within the MESSy structure .

The submodel ConVective tracer TRANSport (CVTRANS) was introduced by to account for convective tracer transport in EMAC. This submodel can reproduce observed changes in the vertical profiles of non-soluble tracers due to convection sufficiently well . It makes use of a single plume/bulk convective transport parameterisation based on the formulation of . applied the convective mass fluxes for the updraft, downdraft, entrainment, and detrainment from the convection parameterisation to calculate the redistribution of the tracers. The mass fluxes must fulfil the following equations, 1aFuk=Fuk+1+Euk+Duk1bFdk+1=Fdk+Edk+Ddk, as described by . F refers to the mass fluxes, D refers to the detrainment, and E refers to the entrainment. The subscripts _u and _d denote the updraft and the downdraft. k indicates the model level. If this relation is not satisfied, the detrainment or entrainment should be adapted accordingly .

Strong updrafts can lead to mass balance problems; i.e. more mass is transported out of a model box as mass is transported into the box within one time step. The mass fluxes are rescaled to prevent a mass imbalance in such cases. This procedure can lead to a damping of the convective transport. To overcome this issue, included intermediate time stepping in CVTRANS to ensure optimum handling of intense convective events.

Note that the transport of water vapour and hydrometeors is not considered in the convective tracer transport algorithm, as the convection parameterisation itself takes care of the redistribution of water species. Some adjustments to CVTRANS were included to increase the physical consistency compared to ; however, these changes do not affect the results of this study substantially (further information can be found in the Supplement).

CVTRANS directly calculates the new tracer profiles. Therefore, it is difficult to analyse the convective transport itself due to the impact of the various background profiles. The convective exchange matrix overcomes this issue. This new tool in EMAC makes use of the same basic principles as the mixing matrix which was introduced by . Firstly, in every vertical model level (1,2,…,N), one pseudo-tracer (P1,P2,…,PN) is initialised with a value of 1 kg m⁻². N denotes the number of model levels. By definition, the vertical model level with the highest number, level N, is closest to the surface. In all other levels, the pseudo-tracers are set equal to zero. The vertical profiles of the pseudo-tracers can be written as N-dimensional vectors. Applying this, the pseudo-tracer P1 is given by P1=(1,0,0,…,0), and P2 is P2=(0,1,0,…,0). Putting all these vectors together results in an N×N diagonal matrix, as can be seen on the left side of Fig. a.

The time integration, i.e. the vertical redistribution by convective transport of the pseudo-tracer field, is performed based on the transport routine in CVTRANS for the convective exchange matrix. The considered processes are shown in Fig. b. The time integration results in the convective exchange matrix (TrMa). The entries of the matrix give the portion of the air mass (mair) that was transported from a specific departure level (given by the pseudo-tracer field in the beginning) to a certain destination level. For example, TrMai,j with i,j=1,…,N describes how much mair was transported from level i to level j. If j=i, then TrMai,i characterises the contribution of level i to level i itself. In other words, it shows the amount of air that was not affected during the convective event. This is illustrated in Fig. c and highlighted in red. The upper-left entries (yellow in Fig. ) represent the transport from a level i to level j with i>j, i.e. the upward transport to level j which started in level i. Thereby, the notation is that the lowest model level has the highest number and the uppermost level is level 1. The downward transport (transport from a lower-level number to a higher-level number in this notation) is marked in blue in Fig. c. An example of a convective exchange matrix can be found in the Supplement for one event (see Fig. S1b).

Figure shows how the convective transport matrix is structured (a) in the tropics and (b) in the mid-latitudes. Again, the highest model level number (31) refers to the level closest to the surface/the level with the highest pressure. This is the case for the destination and origin levels. Roughly the following characteristics of convective upward motion (yellow in Fig. ) are visible in the convective exchange matrix:

Shallow convection and turbulent detainment, when the origin level is located in the boundary layer (BL) and the destination level is also located in the BL or in the lower troposphere.

Three-dimensional global simulations have been conducted with the convective exchange matrix implemented utilising EMAC. A total of 31 vertical pressure levels up to 10 hPa are used, and a horizontal resolution of T63 (triangular truncation with wavenumber 63) has been applied. This is associated with 192 × 96 grid points with areas between 32.5 km × 32.5 km in the polar regions and 207.9 km × 207.9 km in the tropics and a time step of 12 min. Temperature, vorticity, divergence, and surface pressure are nudged towards ECMWF reanalysis fifth generation ERA5; and the sea surface temperature and the sea ice coverage are prescribed by the nudging data. The nudging is based on and applied as described by .

An overview of all submodels used is given in the Supplement (Table S1). The essential ones for this study are mentioned in the following. A basic methane chemistry is applied to take the water vapour production in the stratosphere and its influence on radiation into account using the submodel CH4 . Further considerations of chemical reactions are not necessary, because this study exclusively investigates the redistribution of air masses by convection and not the effect on single tracers. Monthly mean values for greenhouse gases are used to include their radiative effect based on . The climatology is used for tropospheric aerosol as described by . For the stratospheric aerosol radiative effect, optical properties of the chemistry–climate model initiative (CCMI) database are applied, e.g. as in . The submodel CONVECT by is applied with the Tiedtke–Nordeng scheme to calculate the parameterised convective properties needed in CVTRANS to calculate the convective exchange matrix.

The convective transport matrix is shown in Fig.  for the temporal mean of the 10-year period 2011 to 2020 and the area-weighted mean between 60° N and 60° S. The mean transport matrix is shaped by a large number of initial unit matrices because atmospheric moist convection is a rather localised effect. As a consequence, the mean convective transport is not as intense on a global scale as for an individual local deep event (compare Fig. S1b). Nevertheless, the convective transport has a non-negligible effect on large spatial and temporal scales.

The strongest upward transport can be seen in Fig.  starting in the lower free troposphere and in the BL (level 31 to 26) and reaching only into the lower free troposphere (level 29 to 25), representing shallow convection and turbulent detrainment from updrafts. Deep upward transport starts mostly in the same heights (levels 31 to 28) but shows lower fractions than the transport into the lower free troposphere. Starting levels in the free troposphere are associated with lower portions of upward-transported material. The mass-balancing subsidence is the dominant downward transport mechanism over two to three levels below the main diagonal. From the lower- to mid-tropospheric-origin levels, the downdrafts transport air mass especially to the three levels closest to the surface.

Figure shows the temporal and spatial mean convective transport compared between 2011 and 2020 to the reference period from 1980 to 1989. The transport to levels with low pressures (level 4 to 7) increased significantly from all starting levels below the destination levels. The subsidence adapted accordingly. More material descents from levels which are associated with the upper troposphere in the tropics and with the upper troposphere and lower stratosphere in the mid-latitudes (between level 12 and 4).

These features of the difference convective exchange matrix (Fig. ) can be explained considering the frequency distributions of the updraft mass fluxes compared for the reference time period and 2011 to 2020 (Fig. ). In Fig. , the mass fluxes from deep convective events were categorised according to their strength. The lowest class (below 1 × 10⁻⁷ kg m⁻² s⁻¹) contains all no-events, so the cases where no deep convection occurred or the mass fluxes were too small. The class with the strongest updraft mass fluxes contains all mass fluxes which are stronger than 0.2 kg m⁻² s⁻¹. This classification was performed for all height levels. The difference of these mass flux distributions is shown in Fig.  for a selected set of model levels and for the values from 2011 to 2020 minus the ones from 1980 to 1989. For a better visualisation, the symmetric logarithmic difference is shown instead of the absolute numbers. The updraft mass flux in the upper levels (height range of the tropopause) shifts to stronger mass fluxes in the later time period. Moreover, more events reached these levels from 2011 to 2020 in comparison to the reference period. This trend is consistent with the increased transport to the upper level as observed in Fig. .

The enhanced transport to levels roughly associated with the tropical tropopause could be explained by an increase in the strength of the convection or even an enhancement of convection overshooting the tropopause. A non-significant tendency towards more overshooting convection is predicted by the Tiedtke–Nordeng scheme over the 41-year time period. We define one (tropopause) overshooting event as an event when the updraft mass flux associated with one convective event reaches beyond the independently calculated tropopause in one column and at the same time step. It cannot be ruled out that the detected overshooting is only an artefact of the coarse model resolution because both the tropopause height and the mass flux are mean values. It can be assumed that both quantities vary significantly within a box. However, the latter does not affect the convective transport in the model because the transport only sees the grid box mean values. discovered that tropical convection reaching beyond the tropical cold-point tropopause occurred slightly more often in the future scenario (2075–2104, Intergovernmental Panel on Climate Change A1B emission scenario) than in their historical simulations (1979–2008). Concerning this study, the trend in tropopause overshooting convection is not significant. Therefore, it can be ruled out as a primary source for the major increased convective transport to the tropical tropopause/lower stratosphere levels (level 7 to 4).

The model predicts a rise in the global mean tropopause (not shown). A higher troposphere could clear the path for convection with a larger vertical extent, but an increased penetration of convection could also cause a lifting of the tropopause height (for the second possibility, see ). Deep convection tends to occur less frequently (Fig. ), and, for this reason, the increased height of the deep convection can have a rather local impact on the tropopause height. Therefore, we assume that the dominating process is the change in tropopause height, which leads to deeper convection and not vice versa.

The upward transport has decreased from starting levels in the lower troposphere (levels between 31 and roughly 21) to the destination levels in the mid-troposphere and some upper troposphere in the most recent time period in comparison to the 1980s (see Fig. ). Figure  is considered again to examine possible reasons for this decrease in upward transport. Deep updraft convective mass fluxes occurred less frequently in many height levels with relevant values (larger 1 × 10⁻⁷ kg m⁻² s⁻¹) from 2011 to 2020 in comparison to the 1980s. A bimodal trend emerges from Fig.  in terms of the changes in the distribution of the deep updraft mass fluxes. The mass fluxes tend to be either at the stronger edge or zero in the later time period. Higher mass fluxes are generally favoured in the uppermost levels in the later period, shown in Fig.  (level 6). Therefore, the negative trend in some upper-tropospheric levels in Fig.  can be attributed to an increase in the outflow height and a decreasing trend in the occurrence of deep convective events over the 41-year period (Fig. ).

The upward transport increased for two starting levels in the mid-troposphere (levels 20 and 21) on average from 2011 to 2020 compared to the reference period depicted in Fig. . This leads to the hypothesis that mid-level convection occurred more frequently; however, mid-level convection according to the definition in the Tiedtke–Nordeng scheme did not increase in number (not shown). On the other hand, shallow updraft mass fluxes show higher values in the two mentioned mid-tropospheric levels (levels 20 and 21). The same is the case for the mid-level convection. However, the mid-level convection headed towards a more frequent occurrence of the higher mass fluxes for a wide range of altitude levels. These could play a role in this prominent increase in upward transport from these two mid-tropospheric levels (level 21 and 20), but the reason for this cannot be unambiguously clarified at this point.

The downdrafts shift to starting levels located higher above the surface in the later time period compared to the reference period (Fig. ). The impact of downdrafts starting at the mid- to upper troposphere (levels 15 to 13) has increased; i.e. more mass is transported downward from mid-tropospheric levels. On the other hand, the downward motion is reduced for origin levels in the free to mid-troposphere (between 26 and 16) on average from 2011 to 2020. This finding goes well along with the height increase in the deep convective systems.

A strengthening of the updraft detrainment is observed in Fig.  in the lower troposphere (up to level 26). This could be due to an increase in shallow convection because of the water vapour and lapse rate feedback on convection (e.g. , and references therein). However, the global occurrence of shallow convection did not significantly increase during the 41-year period (not shown). This means that either the shallow convection intensifies or the detrainment of mid-level and/or deep convection must increase.

In summary, more material stays at its original level for levels in the BL to mid-troposphere. This trend is significant for many mid-tropospheric levels (between levels 27 and 17). This also points towards an overall reduced deep convective transport.

Figure a shows the difference convective exchange matrix for 30° N to 30° S. Overall, the changes in tropical convective transport match well with the ones for the global case (Fig. ). The convective transport increased to levels up to the tropical tropopause (level 7 and above) from 2011 to 2020 in comparison to the 1980s. The downdrafts also shift to starting levels located further up with regard to the surface, and more mass balancing subsidence is found for the upper-tropospheric to lower-stratospheric levels. In total, more material stays at the starting level and is not affected by the convection for a substantial number of levels. There is only one dissimilarity between the tropical and the global case: the significance of convective transport differences compared to the reference period in the BL (level 31 to 29) increased.

The picture arising for the Northern and Southern Hemisphere extra-tropics seems to alter from the tropical one (Fig. b and c compared with Fig. a). The upward transport is pronounced for a wide range of levels. The tropopause is located mostly at higher pressures in the extra-tropics than in the tropics (Fig.  and Table S2). Considering the differences in tropopause height, the main patterns in convective transport changes are similar in all considered regions compared to the latest 10 years of the simulation with the 1980s: (1) the convective transport to the tropopause region and above is increased. (2) The mass balancing subsidence strengthened from origin levels at about the tropopause height/lower stratosphere. (3) The downdrafts originate at higher levels. (4) Less material from the boundary layer/lower troposphere reaches the free to upper troposphere (up to level ∼ 16). Thereby, the convective transport changes are not often as significant and as much pronounced in the Southern Hemisphere compared to the Northern Hemisphere.

The mean convective transport from the boundary layer to the upper troposphere is calculated for each grid column to assess the regional variability in convective transport. The UT is heuristically defined as the region vertically ranging from the tropopause level (in Pa) down to the level where the pressure is equal to the tropopause pressure plus 150 hPa. The tropopause height and the height of the planetary boundary layer are taken from the EMAC output.

The mean upward transport is not directly comparable to a tracer concentration in the UT or tracer release studies as performed by , , or . Transport by the updraft interplays with the grid-scale subsidence, grid-scale advection, and other processes which lead to a combined impact on the transport of a tracer. The convective exchange matrix opens the possibility to study the upward transport driven by convection undisturbed by other processes and pre-existing tracer distributions. In this section, the focus is on the regional differences and “trends” in the upward transport from the BL to the UT.

The 10-year mean of the BL-to-UT transport (Fig. ) shows a similar structure to the convective precipitation (compare , and their Fig. 8) and the cloud top brightness temperature compare. The values are enhanced in the inner tropical convergence zone, Amazonia, central Africa, and the North Atlantic storm track. Particularly high portions of air mass were transported from the BL to the UT above the Himalayas and the northern to the central Andes mountains. This is not surprising for two reasons: (1) the model levels are compressed above high mountain areas. Thus, the distance between the BL and the UT is reduced. (2) It can be assumed that the Tiedtke–Nordeng scheme does not perform sufficiently well in these areas in general because the precipitation rates calculated with the Tiedtke–Nordeng convection parameterisation within EMAC are too high compared to observations in these areas, as shown by in their Fig. 2. As the freshly formed precipitation is proportional to the updraft mass flux, an updraft mass flux that is too strong results in an overestimation both of the convective precipitation and of the convective upward mass transport. No air masses were transported from the BL to the UT west of Africa and South America at about 20° S (with areas in Fig. ), where subsidence is dominating the large-scale circulation patterns. Small but non-zero values indicate very low (deep) convective activity west of Australia, over northern Africa, and off the coast of California (dark areas in Fig. ).

The change in the mean BL-to-UT transport is characterised by regional differences (see Fig. ). In dependence of the region, the trend is either negative or positive. Overall, the transport from BL to UT was only slightly smaller between 2011 and 2020 than in the reference period. The global (60° S to 60° N) area-weighted average decreased from 0.07909 % per time step (1980 to 1989) to 0.07829 % per time step (2011 to 2020). This seems counter-intuitive at first glance because of the significant increase in transported air masses to the upper levels of the convective exchange matrix (compare Fig. ). First and foremost, the increase in the convective outflow height leads to the increased transport to the uppermost levels influenced by the convection (levels 4 to 7) (in Fig. ), likely due to an increase in the tropopause height. This does not necessarily imply an increased transport into the whole UT.

The mean transport from the BL to the tropopause region remains nearly unchanged. Thereby, the region of the tropopause is defined as the level of the tropopause down to the level with a pressure equal to the pressure at the tropopause plus 50 hPa (in contrast to the UT, which was defined by the tropopause pressure +150 hPa). The mean transported portion was 0.02114 % per time step in the reference period and increased marginally to 0.02118 % per time step from 2011 to 2020. This indicates that less convection reaches the UT in general but that the convective transport to the tropopause region stays similar due to compensating processes: the deeper penetration balances or even exceeds the effect due to the lower occurrence rate of deep convection. We note that these trends are rather small and need to be validated in the future.

The transport to the UT decreases close to the Equator over the Central and Eastern Pacific. North and partly south of this area (at ∼ 20° N and ∼ 20° S), an increase in transport becomes apparent compared to the reference period. A possible weakening and widening of the Hadley cell could explain this trend. In this framework, we cannot confirm or reject this hypothesis.

The problems of the underlying convection parameterisation are an important factor for the convective transport as well. The regions with the largest changes are widely the areas of the least accurate simulations of precipitation by the Tiedtke–Nordeng convection scheme. This convection parameterisation overestimates the precipitation at the Pacific coast of Central America, central Africa, the western Pacific Ocean, and the western Indian Ocean and underestimates the precipitation over the western Maritime Continent, as can be seen in Fig. 2 by . These areas show pronounced changes in the transport of BL air to the UT. These changes, therefore, go along with high uncertainties, which we cannot further quantify due to a lack of global observations of convective transport or mass fluxes.

To analyse whether the regional changes originate from climate change or are due to natural variability, one La Niña event (Fig. S4) is compared with one El Niño event (Fig. S5). For the El Niño event, 1 July 1982 to 30 June 1983 was chosen because identified it as an extreme event. According to , a strong La Niña event took place in 1988 and 1989, and this is chosen because the conditions are very different from the El Niño event. For consistency reasons, we took the second half of 1988 and the first half of 1989 for the La Niña case into account.

The largest differences between the El Niño and La Niña events occurred in the area of the Equator over the Pacific. The mean transport to the UT from the BL differs up to 0.38 % per time step (Fig. ). found an increased number of organised convective events in the same area comparing El Niño events with La Niña events between mid-1983 and mid-2008. This matches with the presented results from this study, that there is more transport into the UT from the BL during the considered El Niño event. A huge decrease can be observed northwards and southwards from the Equator in the Pacific (∼ 20° N and ∼ 20° S) and over the Maritime Continent (0°) when comparing the El Niño event from 1982/83 with the La Niña event from 1988/89 (Fig. ). Overall, the differences between the El Niño event and the La Niña event are much more pronounced than changes in Fig. .