Upper-tropospheric outflow is analysed in cloud-resolving large-eddy simulations. Thereby, the role of convective organization, latent heating, and other factors in upper-tropospheric divergent-outflow variability from deep convection is diagnosed using a set of more than 80 large-eddy simulations because the outflows are thought to be an important feedback from (organized) deep convection to large-scale atmospheric flows; perturbations in those outflows may sometimes propagate into larger-scale perturbations.

Upper-tropospheric divergence is found to be controlled by net latent heating and convective organization. At low precipitation rates isolated convective cells have a stronger mass divergence than squall lines. The squall line divergence is the weakest (relative to the net latent heating) when the outflow is purely 2D in the case of an infinite-length squall line. At high precipitation rates the mass divergence discrepancy between the various modes of convection reduces. Hence, overall, the magnitude of divergent outflow is explained by the latent heating and the dimensionality of the outflow, which together create a non-linear relation.

Organized deep moist convection is not only a substantial precipitation source over the tropics and mid-latitudes but also a driver of the global atmospheric circulation due to its conversion of potential energy into kinetic and moist static energy. This energy conversion is achieved by so-called latent heating: the condensation of water vapour warms rising air parcels while they move upwards, expand, and cool. The warming tendency of latent heating opposes the stronger cooling tendency (expansion) and provides (positive) buoyancy. The positive buoyancy is the fuel to the moist convection that can keep it running, resulting in accumulation and further organizing.
Once organized systems of deep moist convection (from now on referred to as convective systems) have formed, they feed back onto the background atmospheric circulation. The background atmospheric circulation is hardly affected by tiny convective systems composed of one or two cumulonimbus clouds. On the other hand, the mesoscale circulation can be entirely disturbed and even dominated by convective systems of sufficiently large size and intensity

An increase of the flow feedback strength with the amount of net latent heating is supported by the simplified linearized gravity wave model described in

Over the last decade, studies on predictability have suggested that differential upper-tropospheric flow variability induced by organized convective systems can impact the predictability of weather (e.g.

Ensembles and physical perturbations are applied to the following selected organizational modes of convection: a supercell, regular multicells, and a squall line. The latter class is further sub-divided into two categories (finite-length and infinite-length squall lines). Convective momentum transport is purposely switched off or adjusted by

Large-eddy simulations are suitable for the assessment because of the explicitly resolved turbulence and cloud-scale processes represented in those simulations. Therefore, they can be assumed to represent the convective processes in a reliable way (e.g.

The structure of this paper is as follows: in Sect.

The simulations presented in this study are conducted with the cloud-resolving model CM1 version 19.8

In LES mode, a turbulent kinetic energy (TKE) scheme after

The initial thermodynamics are prescribed using the profile of

Overview of all CM1 experiments done in this study. The four scenarios represented in the columns of the display have been introduced in Sect.

A supercell scenario is constructed by applying an initial warm-bubble disturbance. The warm bubble is initialized around the centre of the domain, with a radius of 10 km in the horizontal. It has a bell-shaped amplitude, with a maximum of 1 K at the origin, and

A strong wind shear profile (1, see Fig.

A regular multicell is generated in the same warm-bubble initiation scenario as the supercell case.

Moderate wind shear is applied in combination with the warm-bubble scenario, leading to ordinary regular-multicell convection. However, the easterly inflow at the surface is set to 11 m s

An infinite-length squall line is constructed with a cold-pool-damming scenario, in which, west of the

A moderate wind shear is applied, similarly to the regular-multicell scenario. With this moderate shear, the

Despite the substantial similarity to the infinite squall line, this additional class of organized convective systems is constructed to obtain convective cells arranged in a line but with more potential for outflow in the

To test the robustness of the results, an ensemble is constructed in the following way and for each scenario accordingly: the altitude of the interface between the layers where shear is initially present and absent is perturbed (symbol

Ensemble perturbations for the finite-length squall lines (Sect.

Ensemble perturbations provide a background scatter for the natural variability of upper-tropospheric divergence within close proximity of the control runs, as caused by small variations in initial conditions. After applying interface perturbations, winds are interpolated to the native vertical grid length of the corresponding simulation (100 m).

Two types of physics perturbations are applied. These perturbations are applied for a comparison to the control simulation of each of the three basic modes of convection (Sect.

The vertical advection term in both horizontal momentum equations has been adjusted to 0 %, 50 %, and 150 % of its actual magnitude in another set of experiments to perturb the convective momentum transport. This is done to determine the direct effect of the convective-momentum-transport process on upper-tropospheric divergent outflows. The perturbation is similar to creating an artificial source and/or sink term of horizontal momentum at locations with strong convective motion, which is driven by tendencies caused by vertical gradients in horizontal momentum. Systematic non-linear effects on the mass divergence are detectable if processes other than the intensity of the convection affect mass divergence. Additionally, the role of other parameters such as convective organization and convective momentum transport for the upper-tropospheric divergence can be determined by the comparisons between simulations.

The dataset obtained with simulations introduced in Sect.

The domain size that has been chosen in this study is on the small end for studying the feedback from convective cells to their environment, especially for the supercells and squall lines and during the last half an hour of the simulations. In the regular-multicell simulations, however, the limited domain size should be of no concern in this regard: the convective cells cover only a limited fraction of the 120

To test the effective limitations of the restricted domain and more robustly determine the patterns in our dataset (and herewith strengthen the conclusions), one supercell simulation and one finite-length-squall-line simulation are conducted at an extended domain (200 km by 200 km). The simulation time is extended to 160 min, but the analysis window is restricted to the two time intervals until 120 min. For the finite squall line, the large-domain-simulation configuration is not identical to the reference squall line simulation but uses the conditions for an ensemble member with reduced potential temperature perturbations (maximum 4 K only). This configuration is selected to prevent too much additional convective initiation (secondary) with convective precipitation. Such secondary convective initiation is partially located further away from the squall line. The additional convective initiation makes the evolution of the system less comparable to the ensemble simulations in the reference domain.

Diagnostics that represent latent heating by precipitation, upper divergent outflow, and convective momentum transport are evaluated over two separate time intervals. The first time interval ends after 75 min for the squall lines and after 90 min for the regular multicells and supercells. Diagnostics are also evaluated over the second time interval, running from the end of the first interval until the end of the simulation (120 min). This approach with two time intervals creates temporal subsamples. In the first interval's subsamples, effects close to the selected box boundary are relatively unimportant. On the other hand, such effects have a comparatively stronger impact on the diagnostics during the second time interval. Comparison between the two intervals helps to determine the relevance of, for instance, the propagation of gravity waves influencing the larger-scale environment.

Furthermore, a restricted rectangular horizontal area within the whole domain is selected, over which diagnostics are averaged spatially, further limiting boundary effects. The exact extent of the boxes is depicted in Sect.

In this section, the development of the convective systems is described from an introductory point of view by illustrating the simulated reflectivity and describing the evolution of the precipitation systems (Sect.

Figure

The initial warm bubble is a source of buoyant air around the origin, which can freely ascend. Part of it develops into a deep convective cell, and in the conditions of high shear, it organizes itself as a supercell. After 25 min, the cell develops, and simulated radar echoes appear at 3 km altitude (Fig.

From the warm bubble initialized at the origin, a convective cell is able to develop right next to the origin, as in the supercell simulations (Fig.

After 25 min of simulation, the first echo signals appear at

In the infinite-length-squall-line simulations, deep convection develops along the cold-pool edge, which sits on the

The first precipitation cells appear along the

The evolution of the squall line ensemble spread is discussed very extensively in

The finite squall line starts precipitating after 15 min over a length of about 50 km along the

While the core region maintains its position near the centre of the domain, an extension of the squall line at both ends (

With the development of the arching geometry, the simulated reflectivity signal strengthens, and the convectively active area in the outer regions (close to the northern and southern boundaries) increases as well. The squall line centre region starts to accelerate eastward and moves to about 15–20 km east of the origin over the last 40 min of the simulation. However, this acceleration is mostly restricted to a 30 km region around

Simulated radar reflectivity at 3 km height in the control simulation for each of the four modes of convection. From left to right: supercell

The precipitation cells in all four modes of convection do not move far from their original position near the origin, as displayed in each of the panels of Fig. S1 in the Supplement. As the divergent outflows could reasonably be assumed to be collocated with cumulonimbus clouds (the regions of diabatic heating) and their close proximity and thus with the precipitation signal, net outflow has to (mostly) stick to that region near the central part of the domain. That suggests that an integration over a subdomain of the simulation domain suffices for rigorous assessment of outflow magnitudes in the simulation dataset.

Figure

Comparing the four modes of convection, Fig.

Vertical velocity at tropopause level after 90 min for the control simulations of

The patterns of vertical motion as a consequence of gravity waves and convection occurring in the middle troposphere are discussed in further detail in Sect. S2 of the Supplement. This is the level where the wave amplitude of the fastest mode of gravity waves maximizes.

Figure

Time evolution of mass divergence (convergence) as a function of height for three basic modes of convection averaged over the ensemble (filled) and for the individual members (spaghetti contours – blue:

The ensemble spread is narrow for Fig.

Of particular interest is the mid-tropospheric contour of neutral convergence in Fig.

Moving to panels b and d, with regard to the finite-length squall lines, a substantial amount of ensemble spread is identified (the earlier-discussed ensemble standard deviations of divergence overlap with zero over typical depths of about 700 m, which is smaller than for the infinite-length squall lines). The outflow divergence settles to levels of about 7.5 to about 13 km quite soon and remains at those levels along the outer parts (at the edge of the finite-length squall line). The convergence zone at low levels seems to slowly lift with time in this ensemble, reaching an upper bound of about 7 km after 100–120 min. The divergence signal seems to be much stronger in the edge region of the finite-length squall line than at its centre as well. Even though the time evolution of divergence (convergence) in the finite-length-squall-line-centre simulations shares many similarities with that of the infinite-length squall line, the first hour has a contrasting evolution. Signals are nonetheless rather weak during that hour.

The lower boundary of the integration mask for the upper-tropospheric divergence is best set at 7 km, as this boundary is most suitable for differentiating the regions of convergence and divergence. Therefore, results using this altitude threshold are used for the analysis of the next section (Sect.

Note that the figures illustrate the ensemble spread. That means they exclude simulations with physics perturbations. Especially for these perturbed simulations (notably the

Figure

Full dataset of upper-tropospheric mass divergence integrated over the layers 7–14 km versus net latent heating. Included are 206 records covering four modes of convection during two time intervals. The larger symbols indicate simulation data from extended-domain simulations (eight in total).

More specifically, the initial ratio between mass divergence and column latent heating is much higher for the regular multicells and supercells than for the squall lines. For increased precipitation rates, the ratio apparently decreases compared to that at low latent-heating rates. On the contrary, the same ratio for squall lines even increases with precipitation intensity, although this is not so clear. The robustness of the increment in the ratio between the mass divergence and precipitation rate of squall lines is questionable. The typically lower ratios for the supercell at high precipitation rates reduce the gap between the two regimes at higher latent-heating rates; on the one hand, there is a regime that the supercell and regular multicell seem to follow, and on the other hand, there is another regime that the (infinite-length) squall line seems to follow.

Interestingly, the physics perturbations do not substantially affect the suggested regimes, and resolution also has no noticeable effect in the plane of Fig.

When one now focuses on the finite-length-squall-line simulations (pink and red symbols in Fig.

In general, the full domain integration of the finite-length squall line leads to intermediate behaviour, with the amount of divergence in between the centre and the line end. That is a consequence of averaging over the centre and end regions. Reduced normalized mass divergence at a high precipitation intensity also occurs for the full integration over the finite-length squall lines.

Infinite-length squall lines represent nearly 2D convection (e.g. as in

The initial ratios between precipitation intensity and mass divergence suggest that the low precipitation intensity can obey the following two limit regimes:

a 2D outflow regime with reduced mass divergence

a 3D regime with comparatively increased mass divergence in the outflow region.

Investigating the set of larger symbols in the scatter plot (Fig.

The ordering of the different modes of convection (with regular-multicell, supercell, and finite squall line ends inducing the most mass divergence at a given precipitation rate, followed by the full finite-length squall line, the finite-length-squall-line centre, and, lastly, the infinite-length squall line with the weakest mass divergence) is hardly affected by any of the perturbations among all the simulations (see Fig.

By focusing on the multicell divergences in Fig.

The existence of two outflow regimes (2D and 3D divergence) has been

suggested in the previous section

suggested by analytical expressions of flow perturbations derived from a linearized gravity wave model forced by heating

documented for related pressure perturbations and updraught strengths by

Spatial distribution of filtered divergence over altitudes 7–14 km for a finite squall line during the

Figure

During the second time interval, the

The (mean) divergence in Fig.

Upper-tropospheric outflow from deep convection has been quantified for each simulation by integrating the mean mass divergence in 3D over a region surrounding the convective cells (horizontally) and over 7–14 km altitude. Figure

The procedure has been executed for two time intervals separately: a first time interval where the fastest gravity waves escape the box of integration and a second time interval where a large proportion of the gravity wave signal has escaped that box. Even though some potentially relevant flow effects with consequences for upper-tropospheric (UT) divergence could have escaped this integration box with the gravity waves, the results suggest that this is not the case. That such an escape did not have consequences for diagnosed UT divergence can be justified with the following arguments:

The mechanism of gravity waves is to restore density anomalies with fluctuations, which are averaged out when integrated over longer distances in the quasi-horizontal plane.

The similarity of the ratio between mass divergence and net latent heating (1) during the first and second time intervals for regular multicells and (2) to supercell simulations during the first time interval suggests that an escape of gravity waves plays no role in the mass divergence. It certainly does not dilute the outflow divergence by underdetection.

Mass divergence of updraught outflow cannot initiate at a location outside of the convective cell's updraught itself, and spatial distributions of the winds and cumulative precipitation (e.g. Sect.

Related to the previous argument is that the testing of different integration masks for the large-domain supercell simulation indicates that mass divergence only decreases relative to the precipitation rate (!) when integrating over a too-large domain. This is a sign of a substantial increase in subsidence within the integration mask as soon as the mask is altered; the subsidence develops with gravity wave propagation (see

In Fig.

The strong order in Fig.

The signal of convective organization in Fig.

Figure

The idea of the finite-length-squall-line simulations is that the outer part at both of the squall line ends mimics a regime where convective cells can freely induce their outflow in a 3D space when both ends are combined (as if the centre is removed), as in the case of a multicell and supercell. The centre, however, is geometrically somewhat restricted, as in that of an infinite-length squall line. Infinite-length squall lines only allow for outflow in one horizontal direction. The idea is supported by the magnitudes of two components of the mass divergence in finite- and infinite-length squall line simulations: outflow in the zonal direction exceeds that in the meridional direction by 1 order of magnitude, which is consistent with findings pointed out by

Outflow simulations with expressions based on the numerical model of

The robustness of the results, together with the arguments above, give high confidence in the impact of outflow dimensionality on the magnitude of the divergent winds. Furthermore, the intermediate ratio of mass divergence to precipitation rate at high precipitation intensities compared to the initial 2D (low ratio) and 3D (high ratio) regimes suggests that convective aggregation likely affects the dimensionality of convective outflow in the upper troposphere. Outflow likely adapts to a mixture of 2D and 3D regimes due to the convective organization and interference between outflows of individual cells. When aggregates of convective cells collide with upper-tropospheric outflows of other convective cells, the effective dimensionality would be something intermediate between 2D and 3D: the outflows first collide along the line through the updraughts and become nearly 2D along the line, but on the outer regions, the outflow can still move as if the convective cell was isolated. That corresponds to a nearly 3D outflow regime, and any mixture creates ovals of outflow similar to the finite squall line in our conceptual framework (even if the supercells also reveal such behaviour and collisions of outflow after some time).

The mass divergence found in the dataset (Fig.

The initial 2D and 3D regime behaviour with reduced divergence at higher precipitation intensities due to convective aggregation found in this study contrasts with the modelling and observation studies by

On the contrary, using Fig.

Theoretical 2D squall line models have been extensively studied by Moncrieff and co-authors (e.g.

Theoretically, convectively induced divergence profiles are suggested to mimic 2D or 3D regimes in some cases. On the contrary, in practice, intermediate behaviour is suggested to be more likely, especially for intensive systems. That can be a worthwhile consideration for the development of convective parameterizations that would take convective organization and aggregation into account (e.g.

In

The quantitative understanding of upper-tropospheric outflow and the uncertainty quantification achieved in this work could support an extension of the potential vorticity diagnostics of

LES simulations of four types of convection with ensemble, physics, resolution, and other modifications have shown that upper-tropospheric mass divergence associated with deep convective systems depends on net latent heating (i.e. precipitation intensity) and on the convective organization. Divergent outflows have been integrated over a fixed area and 7–14 km altitude.
Thereby, the main precipitation cores for each type of convection have been covered and split over two time intervals (Fig.

Simulations on extended domains, in addition to an ensemble of simulations, strengthen the confidence in the results. Convective momentum transport plays no direct role in the mass divergence in the simulations. Nevertheless, by affecting the organization and precipitation rates within a convective system, it can indirectly affect upper-tropospheric mass divergence.

An important implication of this study is a potential bias in upper-tropospheric divergent flow if the convective organization is unknown or misrepresented (as is generally the case for parameterization). This implication would exist even if the precipitation rate or some kind of statistical distribution describing the spatial mean and variability of the precipitation rate were known.

The findings are in good agreement with the linear gravity wave adjustment models triggered by convective heating in

Temperature and moisture profile following

North–south profile of initial potential temperature perturbations along the length of the finite-length squall line for five selected model levels, counted upwards from the surface level.

Parts of the output of this study are available for download at

The code in the “Code availability” statement, together with the Supplement, allows readers to download our data from this work (

The supplement related to this article is available online at:

The idea for this study originates from the authors in collaboration with colleagues from TRR 165. The study was designed, conducted, and composed by EG, with contributions from and under the supervision of HT.

At least one of the (co-)authors is a member of the editorial board of

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors would like to thank the collaborators in the Waves to Weather project A1, namely George Craig, Michael Riemer, and Tobias Selz, for their input and, in addition, those who helped the lead author facilitate the initialization of CM1 on the high-performance computer in Mainz, namely Manuel Baumgartner (now at DWD) and Christopher Polster. Lastly, we would like to thank the reviewers for their useful suggestions and the editor for handling the paper.

The authors would also like to acknowledge the computing time granted on the supercomputer MOGON 2 at Johannes Gutenberg-University Mainz (

This research has been supported by the Deutsche Forschungsgemeinschaft (grant no. TRR-165). Holger Tost received additional funding from the Carl Zeiss foundation.This open-access publication was funded by Johannes Gutenberg University Mainz.

This paper was edited by Thijs Heus and reviewed by two anonymous referees.