Analysis of variability in divergence and turn-over induced by three idealized convective systems with a 3D cloud resolving model

The sensitivity of upper tropospheric and lower stratospheric convective outflows and related divergence fields is analysed using an ensemble of cloud resolving model (CM1) simulations in LES-mode including various physically manipulated simulations for three different convective systems initialized with an idealized trigger. The main goal of this study is to assess to what extend the divergence field depends on cloud microphysical processes, the mode of convection and on the processes of convective momentum transport and moist static energy redistribution. We find that latent heat release (representing 5 the microphysical uncertainty) plays an essential role by explaining much of magnitude of the divergence field that will be formed. Convective organisation explains another important fraction of the variability in the divergence field that is formed by a convective system and behaves non-linearly, likely partly via condensation and subsequent (re-)evaporation/sublimation. The detrainment of stratospheric air also shows large sensitivity among the experiments.

. Skew-T diagram of the thermodynamic profile used, after Weisman and Klemp (1982). The red curve shows the evolution of a parcel with ambient conditions that is pushed upward from z = 875 m to its equilibrium level and beyond (without entrainment). On the left, the wind profiles used for the three cases (#1: supercell, #2: ordinary multicell, #3: squall line, #2 and #3 with identical shear) are shown.

Overview of all experiments
To map intrinsic sensitivity and uncertainty related to the reference experiment, an ensemble consisting of the reference run 75 and 9 members has been used for comparison with subsequent experiments. Small perturbations (randomly generated, −5 to +2%, see Table S1 in supplement S1) have been applied to the altitude of the top of the shear layers (z top ) in each wind profile to create initial conditions for each ensemble member. Next, the model has been modified from a physical-dynamical point of view in the following ways for a set of experimental runs:
-Vertical advection of water vapor (VAQ) (-20 and +20%), altering energy (re-)distribution by the convective circulations. 85 All of the altered processes will initiate feedback loops and to some extent behave non-linearly due to an array of instability and restoration mechanisms that act in the atmosphere. (Therefore and) due to resulting chaotic behavior of the atmosphere we cannot fully disentangle the consequences (and also backward: root causes) of differences between experiments and cases.
No other settings than stated in 2.2 and this section have been altered with respect to the supercell simulation, which is included as a test case in CM1. The simulations have been run on Mogon2 in Mainz. For more details on the configuration and relevant 90 files, see code availability. An overview of the experiments is also found in Table S1 of the supplementary material.

Diagnostics
(Horizontal) divergence has been calculated directly from the velocity fields in the output using finite differences on grid points.
Moist static energy (MSE) has been calculated based on grid point values of potential temperature Θ and water vapor mixing ratio r v with a constant C p = 1005.7 J kg −1 K −1 and (modified, but in principle constant) L v of 2.501 × 10 6 J kg −1 .
For the calculation of condensation rates, the CM1 output variable describing instantaneous condensation rate has been used.
For the vertical advection tendencies we implemented a diagnostic in the modified CM1 code, without a divergence contribution (which would then be attributed to divergence rather than vertical advection, as discussed in Arakawa (2004)).

100
A suitable area and time selection over which to integrate and subsequently average budgets of divergence, latent heat release, moist static energy, vertical advection of meridional and zonal momentum is done. To select a representative area affected by convective circulation and its (upscale) propagation, we include most of the region with gravity wave activity excited in the tropopause region ( Figure 2). Triggered gravity wave activity reaches domain boundary within the two hour simulations, since convection initiates in the first hour and the waves propagate with up to about 30 m/s. The obvious effects from the model 105 boundaries have been explicitly excluded as much as possible ( Figure 3).
Since experimental aspects of the simulations make them not nearly identical at given time (except initially), there are some simulations in which the convection initiates earlier or later than in most other simulations, or the excitation and propagation of gravity waves differs from the ensemble. This leads to some inappropriate area selection for some individual runs: for underestimates in the area affected it removes part of the effects from the calculation. The actual effect in these runs will 110 then be underestimated and typically lead to slightly less spread among the experiments, as the excluded effects make such experiments typically more dissimilar to other experiments than diagnosed by missing some effects.

Region of budget calculations
As seen in Figure 2, the near-tropopause region at 11-12 km has the widest area of divergent flow induced by convection.

115
Therefore Figure 3 displays the near-tropopause vertical velocity and the areas selected for the budget calculations for each of the three cases. The black box selections have been used to post-process all of the simulations. For cases #1 and #2 the areas are identical and both evaluated after 90 minutes of elapsed time. For case #3 (squall line), the evaluation is done after only 75 minutes with a different area to limit effects from model boundaries (reflecting part of the waves). Both of the selected areas have nearly identical sizes (7080 vs. 7650 km 2 ).

120
Other (both experimental and ensemble) simulations have been studied to check the applicability of the rectangular areas in Figure 3. In some experiments the area that is subject to gravity wave activity is slightly exceeding the rectangle for the supercell case. This is caused by ensemble sensitivity or by slightly different forcing (experimental runs), leading to slightly different initiation of convective activity and is intended to be taken into account while mapping the sensitivity. The magnitude of deviation from (similarity to) the ensemble hereby helps to interpret behavior of experimental simulations.

Model resolution and case comparison
In Figure 4 we see the vertical distribution of divergence, condensation rate, vertical advection of horizontal momentum (VAUV) and redistribution of moist static energy (MSE) averaged over the regions defined in Figure 3 and the previous section (3.1). In addition we see the ensemble with perturbed runs. As one would expect, a higher degree of organisation (supercell) and a larger area with convection (squall line) lead to larger amplitudes of all processes compared to the ordinary multicell 130 case.
Obviously, the 1 km simulation, having fewer vertical levels, misses the finest details of the higher resolution runs, for example the peak magnitude of the near-tropopause divergence peak for the supercell and ordinary multicell cases. That means that the  Any case lacks substantial VUAV at 1 km and 500 m resolution, which is obviously because (explicit) momentum gradients are not fully resolved on these model resolutions. Additionally, we cannot determine from Figure 4 whether the cubic grid 140 simulations and rectangular gridded reference simulation are sufficiently converged in terms of VAUV.
Particularly the first two cases seem to have converged near the ensemble for the other quantities shown in Figure 4. With reference run and one other ensemble member slightly apart from the other eight the ensemble seems to contain a bimodal distribution in the supercell case, despite relatively strong convergence. However, the ensemble spread is much more pronounced and convergence is not reached for the squall line case.

145
The vertical distribution of divergence due to convection reveals patterns of convective outflow over 8-12 km/350 hPa to the tropopause, with a region of detrainment and mixing of lower stratospheric air (convergence) into the troposphere, where there is still a lot of (divergent) outflow above the tropopause at 12-14 km if convection is well organised (supercell and squall line).
This is due to occasional tropopause overshooting cloud tops and it is also visible in the moist static energy redistribution curves. Accordingly lower and middle tropospheric convergence intensifies with a better degree of convective organisation.

150
The MSE budget shows that both cases with warm bubble initiation (net) extract buoyant air from the boundary layer, as expected. Much of this air penetrates through the middle troposphere and ends up in the upper troposphere as a source of MSE.
The MSE redistribution curve displays the detrainment of stratospheric air mixing slightly warmer air into the troposphere well. For the supercell case the profile has again slightly stronger amplitude than for the ordinary multicell case, as expected.
In the squall line simulations MSE is net hardly extracted from the near surface layer, but rather from just above the boundary 155 layer. Upon inspection of the vertical MSE cross sections perpendicular to the orientation of the squall line (not shown), it is found that even though the near surface layers are a source of buoyant air and thus locally of MSE in this case, the downdrafts initially cause a small MSE increase in the forward flank of the coldpool locally and gravity waves also cause some downward mixing of higher MSE that compensates the small area from which moist static energy is depleted. In addition the simulation domain moves storm relative, which with easterly low level winds means that potential source air (high MSE) is ingested at 160 model boundaries. Nonetheless the MSE gain in the middle and upper troposphere is deeper and has more amplitude as in the other two idealized cases, while the stratospheric extraction of MSE seems comparable to that in the supercell simulations.

Latent heat release experiments
In Figure 5 the result of simulations with modified constants of latent heat of vaporization (lve) are shown. Roughly speaking, an intensification of convection is seen with increasing (lve), which is obviously related to higher values of buoyancy and CAPE 165 with more latent heating. The vertical outflow levels are obviously increasing with latent heating and colliding increasingly strongly with tropopause in the supercell case for simulations with lve > 100% and consequently the divergence is affected accordingly. In accordance with vertical outflow level and magnitude, size of convective cells also clearly correlates positively with increasing lve and more buoyancy and condensation (not shown).
In -40% latent heat constant runs, CAPE is strongly reduced for each case to slightly above 200 j/kg and all of them have 170 much smaller and shallower convective clouds, hardly affecting the near tropopause region. Minor effects on the quantities of interest near the tropopause are visible just for the squall line. In this simulation, moist static energy is net not extracted from the boundary layer, but ingestion of air at the eastern boundary is strong and along with downward mixing of MSE by gravity waves in the wake of the squall line, the net gain in MSE in the lower layers (z < 2.5 km) can be explained.
Comparing the experimental runs with the ensemble, local significant deviation from the ensemble is visually clear for each  of the -40%, -20% and +20%. In case of ordinary multicell convection, all runs are significantly different from the ensemble, while this is less pronounced for the squall line case due to larger ensemble spread.
Particularly strong non-linearity is seen in stratospheric detrainment of high MSE values for the ordinary multicell experiment.
This mixing may potentially significantly affect (prognostic) thermodynamic profiles at near-tropopause level. Figure 5 suggests that isolated convection (supercell and ordinary multicell) is relatively more suppressed when decreasing 180 the latent heat constant with a given amount than the squall line. This is probably due to the stronger forcing of convection when it is initiated with a coldpool in the western half of the domain. It is suggested that forcing and subsequent mode of convection/convective organisation affects the way and magnitude at which convection modifies the atmosphere and subsequently the flow field in different non-linear fashions, given an ambient stratification profile. In other words: how feedbacks between dynamics and the intensity of convective circulations are affecting larger scale flow depends on mode of convection at a given 185 convective instability. We will further explore such non-linearity in Section 3.6.

Momentum advection experiments
It is generally accepted that modification of VAUV affects convective organisation. First of all the genesis of a supercell requires this term in the momentum equations: it is necessary to tilt horizontal vorticity. The interaction of this tilted vorticity with updraft dynamics is necessary for supercell formation Markowski and Richardson (2010). Furthermore, absence of the 190 term in the ordinary multicell and squall line cases limits the role of coldpools in the propagation of the convective system and, in relation to this, limits the tilting of warm air bubbles over the coldpools that feed convective cells. In other words: the easterly inflow east of the squall line cannot be brought upward into the squall line for instance and lead to the typical flow pattern in a squall line Markowski and Richardson (2010). Therefore all VAUV experiments have (strongly) modified convective structures and areal sizes compared to the reference runs.

195
Some interesting consequences of amplified and suppressed VAUV can be identified in Figure 6. Non-linearities affect the diagnosed VAUV (see also Section 3.6). VAUV itself adjusts strongly at near tropopause level if non-zero and near the surface (+50% VAUV run). This can partly be explained by VAUV peaking around these two levels.
Condensation rates ( Figure 6) are either reduced notably ( The supercell case shows that the ensemble members are accordingly most efficient regarding MSE turn-over, with particularly 205 pronounced weakening for no and -50% VAUV. Among the ordinary multicell simulations spread is small for varying VAUV.
For the squall line case, MSE exchange grows monotonically with increasing VAUV, consistently with what is seen in the condensation rates.
Divergence effects resemble those of area mean condensation rates. Generally, adjusted VAUV experiments also tend to dis- tribute the upper tropospheric and lower stratospheric divergence (> 0) over a layer that starts slightly lower, with a smaller peak amplitude. Most modified VAUV runs (except squall line with +50% VAUV) fall with their divergence outside the ensemble range in the upper troposphere and lower stratosphere, which means that momentum mixing by convection has a significant effect on the divergence field locally and particularly on the peak value.

Water vapor advection experiments
In Figure 7 the budgets of simulations with modified vertical water vapor advection are depicted. An important characteristic 215 of the 0.8-run that can be found in all three cases is the occurrence of condensation at near-surface levels, as opposed to all other runs so far. This is because horizontal moisture convergence cannot be completely compensated by upward transport of water vapor before condensing, leading to near-surface hydrometeor accumulation by the convergent flow. This means that the run has physical behavior that is not realistic. The condensation profiles for this run are shifted downward, probably due to the aforementioned effect. The magnitude of total condensation is affected both negatively and positively in the modified water 220 vapor advection runs, depending on the case. This is explained by total area of convective clouds in the three different cases: the supercell becomes smaller with less condensation, while the ordinary multicell shows more condensation and a larger area of convective cells.
With amplified vertical advection of water vapor, we can see strong non-linear increases in condensation, which occur because once a convective updraft establishes it is vertically more permeable to moisture than in the reference run. This also manifests The effects of the 0.8-runs compared to the reference runs regarding the VAUV in cloud regions are seemingly non-linear and correlated to the condensation effects slightly below, with enhancements in condensation leading to higher VAUV and 230 decreased condensation leading to lower values of VAUV. Likewise, the reversed happens when vertical vapor advection is amplified, with momentum mixing increasing throughout the depth of the convective circulation. Many of the divergence effects resemble those seen in VAUV and are therefore similarly related to the condensation rates slightly below.
In principle, there is a direct effect of amplified (reduced) vertical vapor advection on MSE change, i.e. more water vapor advection increases MSE transport and change. Feedbacks such as consecutive phase changes can overcome the intuitive effects 235 and reverse or enhance the net modification in MSE change and subsequently also for divergence. There are clearly non-linear amplification effects in the 1.2-run that impact MSE redistribution and divergence (also evident effects in the condensation profile). On the other hand, the 0.8-run has counter-intuitive/reversing effects in the ordinary multicell case: net divergence is increasing rather than decreasing compared to the reference run, which is related to increased condensation. MSE redistribution is also not clearly weakened. Strong sensitivity to vertical water vapor advection is found in the detrainment of stratospheric air 240 near the tropopause, like in other experiments -most clearly in the ordinary multicell and squall line cases. Additionally, the divergence profile of the 0.8-run with squall line clearly deviates from all other runs. The divergent convective outflow peak falls from 10-13 to 6-10 km, which is partly because cell penetration of the tropopause is delayed (not shown) and the squall line budgets are analysed after 75 minutes, earlier than for the other two cases. While in other simulations net convergence generally still occurs up to around 7-8 km elevation (see Figures 4-7), this specific simulation has its divergence peak around 245 that level. Therefore, the net elevation where the convergent inflow occurs, sinks substantially to below 3 km and convergence below that level intensifies substantially to conserve mass.

Feedback strengths
In Figure 8 some feedback strengths are visualised. The quantities on the y-axis are averaged over the 100-300 hPa layer in this plot and weighted by pressure, i.e. a model layer with more mass is weighted accordingly. In the plot, the (1,1)-points are 250 reference simulations and the (0,0)-point would mean no latent heat release and no divergence in Figure 8a. It can be seen in Figure 8a that the outflow of convection and its divergence in the 100-300 hPa layer is very sensitive to changes in the latent heat constant or equivalently to an altered ambient stratification (see also Figure 5). Furthermore, the squall line simulation behaves differently in terms of feedback strength than the other two cases of isolated convection, with no mass weighted divergence increase beyond the reference simulation in the selected layer for +10% and +20% lve. It should be mentioned that the upper 255 tropospheric and lower stratospheric divergence in convective outflows is sensitive to the layers included in the analysis. When the same computations are plotted over the 400-100 hPa layer for example, the curve would flatten off between 1.1 and 1.2 instead of rising to nearly 1.6 for the isolated convection cases (not shown).
It is also interesting to notice that the ordinary multicell has a negative divergence contribution for a -40% latent heat constant, which is because the divergent outflow is located below 300 hPa (z = 9.3 km, see Figure 5). Therefore, detrainment from 260 around 200-300 hPa causes net downward mixing and convergence in the layers used for Figure 8a. For the other two cases, little happens in the considered layer at a -40% latent heat constant.
In Figure 8b it can be seen clearly that actual amplification of VAUV is non-linearly reacting to amplification factors imposed on it, as described in Section 3.4. The actual amplification factors are clearly dependent on mode of convection and near-linear for the supercell and ordinary multicell simulations, but not for the squall line simulations, where we can see a lot of variability 265 among the ensemble members. Figure 8c shows that eliminating VAUV generally reduces divergence in the outflow layer. While increasing the VAUV, the divergence at first increases, but trajectories via which it increases are variable. The sensitivity of divergence to VAUV is clearly significant (Figure 8c) and suggested to be substantial in well organised convective systems. Since the feedback strengths presented in Figure 8 are depending on many factors, it is not meaningful to generalize much more.

Divergence imposed by convective systems
In Figure 9 the relation between density weighted mean of the divergence over the 6-14 km layer and total condensational heat is shown. The supercell and ordinary multicell convection seem to behave differently than the squall line case. Among the idealized supercell and ordinary multicell convection there is a good coherence between this upper tropospheric (+ lower stratospheric) divergence and condensational heat, whereas the idealized squall line case has an array of ratios between the two 275 (scattering the plot) with less divergence per unit latent heat release than the other two cases. This is likely partly explained by 13 https://doi.org/10.5194/acp-2020-1142 Preprint. Discussion started: 23 November 2020 c Author(s) 2020. CC BY 4.0 License. 14 https://doi.org/10.5194/acp-2020-1142 Preprint. Discussion started: 23 November 2020 c Author(s) 2020. CC BY 4.0 License. Our results suggest that the simulation of organised convection and its divergence field affecting ambient flow depends model resolution, with higher resolution simulations probably accounting better for the processes involved in convection, arguing that turbulence is more explicitly resolved with higher resolution simulations. This is also argued by Bryan et al. (2003). Our study is nonetheless fully a modelling study and additional support (involving observations) for this line of argumentation can 325 be found in Stein et al. (2014) and Hanley et al. (2014). In Stein et al. (2014) it is argued that convective storm structures in a case study over Southern-England converge for simulations at resolutions of 200-100 m with the UK MetOffice model, which is indeed consistent with Bryan et al. (2003), and these converged high resolution simulations represent statistics of three dimensional convective cloud structures in radar detections better than a 1500 m resolution simulation. Despite the former, high resolution simulations tend to have small convective cores with an overestimate of precipitation intensity. In 330 Hanley et al. (2014) this is further elaborated: higher resolution models perform better in simulating convection down to scales below a radius of about 3 km, but while also varying the subgrid mixing length the correct statistical representation of cell size and precipitation intensity is never achieved simultaneously for the two considered cases. Likewise, it is possible that the representation of the full variability of mean upper air divergence and mean condensational heating rate (Figure 9) is not achieved in our experiments, despite the wide range of experiments we did.
In Peters et al. (2019) it is argued that the effect of mesoscale convective systems on the ambient large scale flow is represented much better in models with (partially) resolved convection than in models with parameterized convection over Western Africa.
Consistently with our results, higher resolution simulations clearly induce a stronger upper tropospheric divergence above mesoscale convective systems. However, they compared a month of one day convection resolving simulations (resolution 2.5 km) with hydrostatic simulations in which convection is parameterized (resolution 30 km) over a much larger domain.

340
In addition to the identification of regime-like behavior by Nuijens and Emanuel (2018), such behavior of convective systems has recently also been explored with a many simulations approach (like ours) by Lawson (2019). Very strong indications of regime and tipping point behavior other than the actual formation of convection itself were found, identifying reflectivity objects as convective elements. Our results can complement this study, in which intervariability among convection in nearly similar environments has also been tested, but none of the experiments had a (very) strong forcing. Our squall line experiments 345 suggest that regime behavior may exist in a forcing continuum as well, among the many degrees of freedom that atmospheric convection has.

Ensemble perturbation saturation
One might wonder whether the initially tiny perturbations actually saturate to the intrinsic variability and the envelop of samples that is statistically of interest with our initial conditions: in other words whether the predictability at the end of the run 350 vanishes and a full (non-linear) regime is appropriately sampled. The applicability of our ensemble can be checked regarding that question. Quantitatively a statistical estimate can be made to address this applicability problem.
To illustrate non-linearity and saturation of twin (perturbation) experiments, Hohenegger and Schär (2007) use a correlation measure: from two initially opposing temperature perturbations (equal, but one of negative and one of positive sign) in their ensemble, Hohenegger and Schär (2007) subtract a reference run temperature to obtain two difference fields (as a function of 355 time). Then, they compute the evolution of the correlation of these two difference fields in time. They also derive that starting from -1, the correlation coefficient between the two difference fields should approach 0.5 after the errors become random fields that saturate as a consequence of non-linear behavior (Hohenegger and Schär, 2007) (derived in their appendix). We have followed a similar procedure for u (perturbed in our ensemble): we made pairs and derived difference fields with a common reference. Since our ensemble is randomly and non-monotonically (monotonically, except variations in z top ) perturbed (see 360 2.3 and Table S1 (supplement) includes the exact numerical values of perturbations), the correlation coefficient can start both near -1 and +1, but not exactly at these values. All of the 12 evaluated pairs except one show similar behavior: difference fields start near ±1, are nearly constant during the first 10-25 minutes and then quickly move to a value near +0.5, reach this value after about 40 minutes and stay particularly close to +0.5 from 70 to 115 minutes (t = 120 minutes was not evaluated). The sole exception is the squall line case ensemble 1 and 9 pair due to a near-identical random perturbation (see Table S1: ENS_01

365
& ENS_09), such that they have initially a nearly perfect correlation and diverge to correlations of 0.66-0.71 during the 70-115 minutes interval. The correlation plot for all pairs is shown in (Figure) S2 of the Supplementary material. The behavior suggests that the ensemble is not underdispersed and suitably examines the uncertainty margins we are interested in.

Summary & outlook
We have tested the sensitivity of upper tropospheric and lower stratospheric convective outflows and corresponding divergence 370 fields for three different convective systems initialized with an idealized trigger. This was repeated with as an ensemble experiment and with various manipulated simulation settings to improve understanding of the generated divergence and its sensitivity and to assess the relationship with the amount of condensate and some feedbacks. The overall goal was to explore to what extend the divergence field depends on latent heating, convective organisation and on the processes of convective momentum mixing and water vapor/moist static energy redistribution.

375
Our experiments with cloud resolving model CM1 demonstrate that there is substantial uncertainty in upper tropospheric and lower stratospheric divergence fields arising from idealized cases of deep convection, particularly for the idealized squall line simulations (larger ensemble spread). The three cases demonstrate that uncertainty in latent heat release (which can be understood as level of detail in the convective cloud microphysics (especially in parameterised convection) plays an essential role by inducing the shape and explaining well the magnitude of the divergence field that will be formed, especially for idealized 380 isolated convection (Figure 9).
Even though some of our simulations ignore conservation laws and are clearly unphysical, the resolution and latent heat and (reference/)ensemble experiments should compare well to realistic uncertainties. Some divergence uncertainty can seemingly be attributed to mode of convection, with embedded processes as underlying causes for differences between these modes of convection. Two mechanisms are thought to potentially govern discrepancy in divergence fields between the squall line simu-385 lations and isolated convection cases: -Recycling of water vapor after condensation (higher fraction in squall line) -Redistribution of moist static energy by the convective system itself, although it was suggested that this mechanism is statistically indistinguishable or absent -Yet untracked interactions which take place due to the discrepancy between idealized warm bubble and coldpool forcing 390 Several other conclusions can be drawn regarding processes affecting the upper air divergence field induced by convective systems: -Convective momentum mixing is shown to feedback on the convective system via circulation sizes of individual cells and organisation and affects the divergence field.
-The latent heat experiments show that given a certain latent instability, the measure of non-linear response of the diver-395 gence profile is depending on factors such as mode of convection.
-Another process that has an important non-linear role is the detrainment of stratospheric air into the troposphere, affecting Θ and q v fields. This non-linearity is revealed most clearly by MSE redistribution in the experiment where water vapor advection is adjusted.
initialization to near the tropopause, where substantial flow uncertainty may accumulate due to variability and/or misrepresentations of convection. The latter is consistent with Baumgart et al. (2019), where it is shown that the very short term errors are induced (< 12 hours) by the convection schemes in ICON and that these subsequently rapidly magnify in the near-tropopause region. Consistently with their results we find that errors caused by uncertainty in the behavior of convective systems can accumulate as divergent flow near the tropopause, which supports that near-tropopause errors (Baumgart et al., 2019) can at 405 least partly relate to earlier convective errors. In addition stratospheric detrainment by mixing of air around convective systems is shown to be able to significantly affect the tropopause region (MSE/energy distribution).
The methods applied here may serve as additional strategies to explain a forecast bust, such as the one documented by Rodwell et al. (2013). In such cases applying a simulation strategy similar to ours to specific convective systems can help to find out whether it is possible to attribute and potentially map the contamination of specific convective systems over the USA to flow