1. Introduction
Fan and Khain (2021, subsequently FK21) comment on our recent paper, Grabowski and Morrison (2020, subsequently GM20), that presents numerical simulations addressing the impact of ultrafine cloud condensation nuclei (CCN) on deep convection. GM20 follows our previous studies that investigate the proposed convective invigoration, such as Grabowski (2015, G15 hereafter) and Grabowski and Morrison (2016). The overall spirit of FK21 is that invigoration has been proven by previous observational and modeling studies, and there is something wrong with the GM20 simulations, for instance, a modeling framework that is too simple (applying bulk and not bin microphysics), or using an idealized modeling setup rather than realistic meteorological conditions. We strongly disagree. We insist that there are fundamental problems with the simplistic “cold invigoration” argument from Rosenfeld et al. (2008), Fan et al. (2013), and others that FK21 seem to take for granted. Our previous simulations agree with theoretical arguments discussed in section 2 of GM20. We cannot accept the argument that the number of previous studies suggesting invigoration is so large that the concept has to be considered proven. Although for brevity we do not review all those studies, we present in the next section key arguments why at least some of them can be interpreted in a different way. Sections 2 and 3 reiterate points made in G15 and GM20 concerning cold invigoration, and present a more general context for the role of cloud microphysics in the invigoration conundrum. We reply to FK21’s comments concerning “warm invigoration” below the freezing level in section 4. We offer a different interpretation of warm invigoration centered on the role of supersaturation changes in polluted conditions, and also discuss some possible concerns about the supersaturation calculations from FK21 (either during model run or in the diagnostic quasi-equilibrium supersaturation derivation) in the appendix. Section 5 focuses on FK21’s comments concerning our simulation technique referred to as the piggybacking that we use to investigate convective invigoration in our past simulations. A brief summary in section 6 concludes the paper.
2. Convective invigoration: Fact or fiction?
First, we have to stress that this exchange concerns a very specific aspect of convective invigoration: the suggested increase of the convective updraft speed in response to microphysical processes. This is only a small aspect of a more general problem of aerosol impacts on clouds and climate, both direct and indirect, as discussed, for instance, in Stevens and Feingold (2009). Because convection responds to environmental conditions (e.g., the temperature and moisture profiles prior to convection onset, large-scale destabilization) one should distinguish between “stronger convection” versus “more convection” paradigms. Both provide more latent heating in a given meteorological situation, but the latter assumes no change in the convection strength while the former does. The “more convection” paradigm can explain the surface rainfall increase with increasing CCN concentrations in some model simulations where updraft strength changes little (e.g., Wang 2005, see Figs. 10 and 11). Idealized simulations in Robe and Emanuel (1996) suggest that the “more convection” paradigm is appropriate for the radiative–convective equilibrium (RCE). RCE is a theoretical paradigm for a tropical atmosphere, where large-scale radiative cooling is balanced by the latent heating of precipitating convection. The “more convection” paradigm is consistent with the RCE study discussed in van den Heever et al. (2011) as the changes to simulated convection strength are rather small. GM20 argue that the “more convection” paradigm also explains the observed impact of ship emissions on convection changes over major shipping lines (see the discussion in section 6 therein).
We feel strongly that invigoration—the increase of the updraft speed in polluted conditions—has not been proven in observations. The key problem is with the attribution of observed cloud changes (like the increase of upper-tropospheric cloud fraction) to the changes in aerosols alone. As argued in Grabowski (2018), it is virtually impossible to eliminate meteorological factors that affect moist convection independently of aerosols. For instance, aerosols can covary with meteorological conditions and separating the two factors can be difficult. See Varble (2018) for additional discussion and examples. Long-term satellite observations can eliminate meteorological interferences, but they do not observe updraft strength directly. Instead, such studies assume that the observed cloud changes are associated with changes of convection intensity (e.g., Koren et al. 2010; Storer et al. 2014). As shown in GM20 [and in Morrison and Grabowski (2011) and Grabowski and Morrison (2016)], an increase of the anvil cloud fraction can come from microphysical consideration alone, namely, smaller ice particles persisting longer in the upper troposphere due to their smaller sedimentation speed. Moreover, an increase of the anvil cloud fraction can also come from situations of “more convection.” See Grabowski (2018) for further discussion why observations alone cannot prove or disprove the invigoration hypothesis.
Observations do provide hypotheses that need to be tested using theory and modeling. One of the first publications suggesting the strong impact of pollution on convective dynamics is the observational study of Amazon clouds in Andreae et al. (2004). They say in the abstract, “Elevating the onset of precipitation allows invigoration of the updrafts.” There are numerous subsequent papers that repeat this claim as discussed in more detail in Rosenfeld et al. (2008). The argument taken word by word from Fan et al. (2013) is that “aerosols delay conversion of cloud water to warm rain due to reduced cloud drop size, allowing larger amounts of cloud water to be lifted to the upper levels that, upon freezing, release more latent heat, and invigorate convection.” Several papers repeating this argument are cited in FK21. But such a “cold invigoration” argument excludes the impact of condensate weight carried through the freezing level, exactly the point of our argument detailed in section 2a of GM20 [and mentioned in our previous publications, e.g., Grabowski and Morrison (2016) or Grabowski (2018)]. If the invigoration argument has merit, it should also work in simulations with a simple microphysics scheme as long as the scheme mimics the delay in the precipitation onset below the freezing level, and shifts precipitation formation upward where ice processes take over. But it does not work as shown in G15. We emphasize that the weight of condensate carried through the freezing level is approximately (approximately, not exactly) balanced by the latent heat of freezing. That is, if pollution reduces warm rain production and leads to more condensate lofted above the freezing level compared to pristine conditions, the impact on buoyancy is negligible because the latent heating from freezing of the additional condensate is approximately balanced by its weight (note that FK21 also mention the role of riming in this mechanism, but from the standpoint of buoyancy the direct impact of riming is no different from freezing). The only way that invigoration is possible from this mechanism is if freezing is followed by rapid off-loading of frozen condensate. However, as we discuss in the next section, such latent heating can induce a larger-scale circulation with the cloud-free environment. This can in turn enhance convection, though there are indications that such enhancement leads to “more convection” rather than “stronger convection” as discussed in section 6 of GM20 and shown in Morrison and Grabowski (2013, Fig. 9 therein). Note that other invigoration mechanisms involving ice processes are theoretically possible, for example, if freezing of cloud water occurs at lower levels in polluted conditions giving a “boost” to buoyancy from latent heating without directly impacting the condensate weight. Thus, our criticism based on the theoretical argument above pertains specifically to the cold invigoration mechanism of lofting and freezing of additional cloud water. That said, our simulations in GM20 and in previous papers also do not support any other cold invigoration mechanisms.
Because observations alone can only be used to hypothesize possible cloud–aerosol–convection interaction mechanisms, numerical modeling is the key. One of the first publications investigating the invigoration hypothesis and often cited as a proof of invigoration (including FK21) is Khain et al. (2005). Khain et al. use a comprehensive bin microphysics scheme and thus can explore microphysical effects with confidence. They use a two-dimensional framework—which is a minor deficiency—but they also apply computational domain with open lateral boundary conditions. This is critical because open lateral boundaries allow development of the flow in and out of the computational domain and formation of the mean ascent inside the domain. In other words, the model simulates not only a convective response to changes in the cloud microphysics, but the combined response of the cloud and its environment. However, the environmental response is highly uncertain because it depends on the details of the lateral boundary conditions. Figure 17 in Khain et al. (2005) shows that the surface rain accumulation after 4 h in the continental (polluted) conditions is over 3 times larger than in the maritime (clean) environment. This is really “flood versus drought” to use the phrase from the title of Rosenfeld et al. (2008). Khain et al. (2005) show changes in the maximum vertical velocities (see Figs. 11 and 12 therein), but these seem more consistent with the “more convection” rather than “stronger convection” paradigm.
Can simulations applying comprehensive numerical models and realistic meteorological conditions provide a proof of convective invigoration? We are not sure. Seifert et al. (2012) and Fan et al. (2013) show a rather small impact on the cloud dynamics and surface precipitation, but a significant microphysical effect that results in large differences in simulated cloud properties between pristine and polluted conditions. Gayatri et al. (2017) discuss observations and numerical model simulations [applying the WRF Model with Khain et al. (2005) bin microphysics] of precipitation processes over Indian subcontinent. They compare rain accumulations over the entire computational domain and over a smaller higher-resolution nested subdomain covering the region with available observations. The accumulations over the entire domain increase a mere few percent [i.e., comparable to those shown in Seifert et al. (2012), see Fig. 9 therein] when CCN is increased from 100 to 3000 cm−3. However, the accumulation over the observational subdomain increases stronger, up to 30%, with the CCN increase, see Fig. 8 therein. The increase may come from different flow realizations between different simulations or from a mesoscale circulation that develops between the subdomain and the outer domain. The velocity statistics (see Fig. 11 there) seem inconclusive. Fan et al. (2018) use similar nested-domain bin simulations (using higher spatial resolutions) and conclude that there is a significant invigoration not only above the freezing level, but also below [the latter also suggested by analysis of simulations discussed in Grabowski and Morrison (2016) and GM20]. Some of the observed (Fig. 2 in Fan et al. 2018) and simulated (Fig. 3 therein) cloud changes, such as close to doubling of the vertical velocities, can in our view only be explained by different cloud-scale or mesoscale flow realizations.
One needs to realize that atmospheric conditions in realistic model simulations, such as in Gayatri et al. (2017) or Fan et al. (2013, 2018), feature atmospheric dynamics almost as complex and unpredictable at small scales as the real atmosphere, with gravity waves, cold pools, mesoscale circulations, individual clouds affecting flow and subsequent cloud evolutions, etc. Untangling such interactions and their impact on cloud evolutions in realistic model simulations, featuring different cloud realizations, provides a challenge not much different than analysis of observations. This is where the piggybacking methodology that FK21 criticize can prove very useful. We also point to the utility of ensemble modeling approaches for detecting a robust signal from the noise of different realizations (e.g., Flack et al. 2019), with small ensembles employed in GM20 as well as our previous papers with piggybacking.
3. How do the microphysics affect moist convection?
G15 and GM20 apply a daytime convective development case from Grabowski et al. (2006). The case is based on observations in the Amazon during the LBA field project. The simulations feature a periodic computational domain, so neither problems with open lateral boundaries nor issues with nested domains are of concern. The 12-h-long simulations start with the observed morning sounding and are driven by evolving surface latent and sensible heat fluxes that strongly increase with the daytime insolation. No radiative processes are included, so the only differences in simulated convection come from different microphysics parameterizations. A relatively simple single-moment bulk microphysics, referred to as Ice A and B (IAB; Grabowski 1999) is applied in G15. IAB includes a simple warm-rain parameterization with a prescribed droplet concentration, 100 versus 1000 cm−3 to mimic pristine versus polluted conditions that affect conversion from cloud water to rain. IAB uses saturation adjustment to calculate cloud water condensation and evaporation. The ice parameterization is simple and links only indirectly to the assumed droplet concentration. The GM20 double-moment (2MOM) microphysics scheme is more comprehensive. Droplet concentration is predicted, as well as in-cloud supersaturation. Droplet condensation and evaporation are calculated explicitly from the predicted supersaturation field instead of relying on saturation adjustment (Morrison and Grabowski 2007, 2008a). We track the depletion of CCN from activation and removal in clouds by predicting the number mixing ratio of already-activated CCN as described in Morrison and Grabowski (2008a); FK21’s description of our approach is incorrect. This method implicitly accounts for aerosol size (or CCN that are more/less readily activated) by predicting the number of previously activated CCN rather than the aerosol number concentration itself. Outside of clouds the number of previously activated CCN is reset to zero; in effect, aerosol reverts to its background characteristics [see Morrison and Grabowski (2008a) for details]. The double-moment three-variable ice microphysics of Morrison and Grabowski (2008b) is closely linked to the warm-rain processes, the predicted droplet concentration in particular. See G15 and Grabowski and Morrison (2016) for more details.
The key results relevant to the discussion here are shown in Fig. 1. The first key point is that there is no “cold invigoration” in either scheme as the updraft statistics between pristine (PRI) and polluted (POL) in IAB as well as between PRIS (pristine) and ADCN (additional ultrafine mode of CCN) in 2MOM differ little in the upper panels. GM20 also considered cases with a modified mean flow, without vertical shear and with no wind (section 5 therein). Vertical velocity statistics from those simulations are similar to those in the right panels of Fig. 1 (not shown). Moreover, G15 also considered yet another bulk scheme for which the velocity statistics are different from those in Fig. 1, but again with small differences between pristine and polluted (not shown). The key point is that the updraft statistics in Fig. 1 do differ between IAB and 2MOM, with stronger updrafts in IAB, especially for the largest vertical velocities. It follows that differences in the representation of microphysics do matter, in agreement with the discussion of FK21. The differences below the freezing level between IAB and 2MOM are likely because of the saturation adjustment in G15 and predicting the supersaturation in GM20. The latter impacts the buoyancy as argued in Grabowski and Jarecka (2015) and in Grabowski and Morrison (2017).
Comparison of hour-by-hour updraft velocity statistics from G15 and GM20: (bottom) 3 and (top) 7 km height. (left) IAB polluted (POL; blue color) and pristine (PRI; red colors) simulations in G15. (right) Two-moment (2MOM) ADCN (blue) and PRIS (red) simulations. Asterisks represent median values, thick lines mark the range between the 10th and 90th percentiles, and circles show the mean updraft velocity. Boxes represent the range between the mean and plus and minus one standard deviation. Data come from 10 time levels for each hour taken from all ensemble members. Only points with vertical velocity larger than 1 m s−1 and total condensate larger than 1 g kg−1 and are included in the statistics.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0315.1
Andreae et al. (2004) and Rosenfeld et al. (2008) correctly argue that freezing of the additional liquid water carried across the freezing level in a polluted environment results in enhanced latent heating aloft and reduced latent heating below compared to the pristine environment. This is because warm rain processes below the freezing level are shifted to ice processes aloft in polluted conditions, with ice falling through the melting level providing the cooling beneath. As long as there is no ice reaching the surface, the total heating within the column does not change, but its vertical distribution is modified. Figure 2 shows the ensemble-averaged 12-h temperature difference between polluted and pristine conditions from GM20 together with the 12-h averaged cloud fraction profiles. The temperature difference is calculated by subtracting the final pristine temperature profile from the polluted one. The profile also excludes the vertical mean temperature change (~0.02 K) that represents a small difference in the total surface rain accumulation (i.e., the total column heating) between polluted and pristine conditions. The cloud fraction panels show that these are almost the same in the lower and middle troposphere, and the main difference is in the upper-tropospheric anvils. The temperature difference at hour 12 between polluted and pristine conditions shows a dipole below 10 km, with cooling below and heating above. This is exactly the impact of the latent heating difference resulting from the shift of precipitation processes from below to above the melting level in polluted conditions. The upper-tropospheric difference comes from microphysical considerations as argued in Grabowski and Morrison (2016) and GM20: smaller ice crystals in polluted conditions extend the anvil coverage and lead to more cooling because small ice crystals sublimate more readily.
(left),(middle) Cloud fraction profiles averaged over 12 h and seven ensemble members in GM20 simulations. Dashed lines are included to better expose profile differences. (right) Ensemble-averaged polluted minus pristine temperature difference at hour 12. Dashed line marks the zero line. The arrows show large-scale motion required to maintain the initial temperature profile in the polluted case. See text for the discussion.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0315.1
The G15 and GM20 simulations are run for 12 h only. However, over longer time scales one can argue that the heating differences illustrated in Fig. 2 will drive a large-scale circulation in the polluted case to maintain the same temperature profile. This is the correct interpretation of the convection–environment interactions; see the discussion in Emanuel et al. (1994). Another interpretation is that the development of such a circulation in the polluted case is consistent with the so-called weak temperature gradient (WTG) approximation appropriate for the tropics (Sobel et al. 2001). One can derive the vertical velocity that is needed to balance the differential heating shown in Fig. 2, with updrafts (downdrafts) driven by positive (negative) heating perturbations as shown by blue arrows in the right panel of Fig. 2. For the small temperature change shown in the figure, the velocities are very small, below 10−3 m s−1. However, the temperature difference scales with the surface precipitation rate. In the LBA case, the mean surface rain accumulation is around 3 mm in 12 h. This is comparable to the mean precipitation rate in RCE simulations in van den Heever et al. (2011). That study features bands of deep convection with local rain accumulations several times larger than the mean. It follows that the ascent–descent pattern within convection bands has to be significantly stronger in the case of van den Heever et al. (2011) simulations, on the order of 10−2 m s−1. Such vertical velocity perturbations significantly affect moist convection (e.g., Grabowski 2018; Kurowski et al. 2020). Simulated changes between shallow and deep convection within convective bands deduced in van den Heever et al. (2011, see Fig. 4 for example) are consistent with large-scale vertical velocity pattern shown in the right panel in Fig. 2. A similar argument applies to the results presented in Sheffield et al. (2015, see Figs. 2 and 3, Table 1). Morrison and Grabowski (2013) show that a similar circulation develops in idealized mesoscale simulations where the convective heating perturbations mimicking the polluted versus pristine difference are applied only in a part of the horizontal domain, see Fig. 10 therein.
An important point is that cloud microphysics does matter for the differential heating shown in Fig. 2. For instance, for the IAB simulations of G15, the temperature difference between pristine and polluted simulations features cooling below and heating above the freezing level, but details of the pattern are different compared to Fig. 2. Bin microphysics with even more elaborate representations of liquid and ice processes, as discussed in FK21, would likely impact the differential heating shown in Fig. 2 as well, and thus affect the large-scale circulation and convection. In short, we argue that the RCE/WTG thinking calls for considering pristine–polluted convective heating changes in the context of the interactions between a convective system and its cloud-free environment. For even longer time scales, changes in the mean cloud fraction profiles illustrated in Fig. 2 affect radiative transfer and thus the mean environment in which convection develops. For unchanged surface condition, this explains differences shown in Table 3 of van den Heever et al. (2011).
4. Warm invigoration
The discussion in FK21 concerning warm-phase invigoration misses the point GM20 make in section 2b therein. FK21 focuses on the validity of the quasi-equilibrium supersaturation in deep convection simulations. In GM20, we question repeated statements in the literature regarding how increased CCN affects the condensation rate. For instance, Sheffield et al. (2015) say in the abstract, “Enhanced vapor depositional growth on the populations of more numerous, smaller cloud droplets in the polluted conditions, and the subsequent increase in latent heat release in the warm phase regions of the cloud, is found to be important factors in convective invigoration of these cloud systems.” This is similar to what Fan et al. (2018) say in the caption to their Fig. 1 as cited in section 2b of GM20. Igel et al. (2015) argue that a twofold increase of the droplet radius for the same water content reduces the condensation rate by a factor of 4 (see Table 1 and the initial paragraph of the discussion section there). However, these statements do not consider the change of the supersaturation in response to the larger droplet size and reduced droplet concentration. In particular, if one takes the quasi-equilibrium supersaturation as a valid approximation, the condensation rate remains the same! This is because, as we show in section 2b of GM20, the condensation rate depends only on the updraft strength as long as the supersaturation is equal to its quasi-equilibrium value. Therefore, differences in condensation rate for the same updraft strength in polluted versus pristine conditions can only occur to the extent that the actual supersaturation deviates from the quasi-equilibrium supersaturation. Such deviations indeed do occur in the GM20 simulations and explain the weak invigoration seen below the freezing level, as shown in the appendix. The key point is that for a given updraft vertical velocity, when considering condensation rate, differences in supersaturation at least partially compensate for aerosol-induced microphysical changes; exact compensation occurs when the supersaturation is equal to its quasi-equilibrium value. This presents a different picture from the studies cited above.
We also emphasize that the primary variable directly affecting cloud dynamics is not the condensation rate per se but rather the buoyancy. Buoyancy is affected by the magnitude of the supersaturation (actual, not quasi equilibrium), and it is larger when the supersaturation is smaller, especially in warm temperatures. The actual mathematical derivation is presented in Grabowski and Jarecka (2015) and examples of numerical values relevant for deep convection are shown in Grabowski and Morrison (2017, see Fig. 2 therein). Differences in the supersaturation affect the Lagrangian history of the temperature, water vapor, and cloud condensate within a convective updraft, an aspect that we are further investigating in current work and will report in the near future. In summary, we agree with FK21 about the existence of a weak warm invigoration mechanism, but question its explanation in the publications mentioned above. That said, there are some specific aspects of the supersaturation discussion in FK21 that need to be clarified. Since these are only indirectly related to the invigoration discussion here, we discuss them in the appendix.
5. Piggybacking
FK21 provide an extensive discussion of the piggybacking technique that was used in G15 and GM20 as well as in other previous publications; see Grabowski (2019) for further discussion. We agree with FK21’s general points concerning piggybacking. Specifically, we agree that invigoration cannot be proven or disproven by using piggybacking. Rather, piggybacking is a diagnostic method that can be used to elucidate mechanisms driving the simulation differences. The case in point: we have referred to piggybacking only briefly above, at the very end of section 2. One can argue that the information piggybacking provides can be obtained by an appropriately design conditional sampling of cloudy volumes within a large ensemble of simulations. For instance, for the case of invigoration, one can sample buoyancy below and above the freezing level to study warm and cold invigoration hypotheses. But how to select points that are mirror images in different convective cloud realizations to obtain a meaningful comparison? And how to exclude different histories even if those images are similar? Piggybacking allows such a comparison by having two sets of thermodynamical variables, one driving the simulation and the other one piggybacking the simulated flow (see Grabowski 2019).
As shown in section 3 above, we test the invigoration hypothesis by comparing vertical velocities in periodic-domain simulations with convection forcing coming from prescribed surface fluxes (i.e., the same in pristine and polluted conditions) where the only difference is the representation of CCN impacts on cloud processes. To explain the differences (or lack thereof), we use piggybacking and compare buoyancy between drivers and piggybackers. We find driver–piggybacker differences consistent with the simulated impacts on the vertical velocity statistics. In summary, we agree with FK21’s discussion, but we do believe that piggybacking is a useful methodology as documented in several publications reviewed in Grabowski (2019). This is especially true in cases where the impact on the dynamics is relatively minor, that is, the driver–piggybacker buoyancy differences are small. This is indeed the case for the simulations in GM20 (see Fig. 5 therein).
6. Conclusions
In summary, we do not agree with the general spirit of FK21’s comments. We feel our arguments presented in section 2 of GM20 are valid. We question the “cold invigoration” mechanism of lofting and freezing of additional cloud water in polluted conditions (e.g., Rosenfeld et al. 2008; Fan et al. 2013) and argue that previous studies attributing results to this mechanism likely come from an incorrect interpretation of observations and model simulations. The modeling framework used in our studies documents no invigoration above the freezing level. We suggest a simple explanation in GM20 consistent with a theoretical analysis of the buoyancy: the latent heat of freezing aloft merely compensates the effort to carry the additional liquid condensate through the melting level. This invigoration mechanism is only theoretically plausible if freezing is followed by rapid offloading of the frozen condensate, but we do not see clear evidence that this occurs generally. In fact, if the freezing of additional cloud water lofted in polluted conditions occurs well above the freezing level, one would expect a decrease in buoyancy because the weight of the additional condensate is only compensated by latent heating once the cloud water actually freezes.
Details of the microphysical parameterization do matter for the specific updraft statistics as shown in Fig. 1, but the pristine–polluted contrast aloft is small. This seemingly contrasts with results from FK21, but caution should be exercised in drawing broad conclusions because different case studies were simulated in their study and ours. To confirm if indeed the bin microphysics scheme of FK21 produces substantially different results from ours, and, if so, to understand what drives these differences, we advocate using the same modeling setup. We agree with FK21 that the Weather Research and Forecasting (WRF) Model would be a good framework for such a comparison. However, we argue that it would be better to start with a simple idealized case rather than the real case setup from the Green Ocean Amazon (GOAmazon) campaign suggested by FK21. This would make it much easier to understand simulation differences, which could also be facilitated by piggybacking.
We agree with FK21 on the merit of “warm invigoration” consistent with the GM20 simulations. However, we question simplistic arguments about increased condensation leading to the invigoration because the correct variable to consider is cloud buoyancy. Following GM20, we argue that changes in supersaturation between pristine and polluted conditions, and their Lagrangian history within a convective updraft, provide a correct interpretation of “warm invigoration.” We also agree with FK21 that piggybacking cannot prove or disprove the invigoration mechanisms, but we insist that the technique is useful in understanding microphysical differences that can lead to the differences in the dynamics.
A specific area where cloud microphysics matters is the interaction between cloud systems and their environment. This aspect was not discussed in FK21, but we feel one needs to consider such interaction to put the impact of microphysics in proper context. Specifically, we stress that the difference between convection developing in pristine and polluted environments primarily affects the vertical distribution of latent heating. For the case of radiative–convective equilibrium, differences in the latent heating distribution require adjustments to the large-scale circulation linking the cloud-free environment with convection. The differential heating deduced from our simulations (suppressing convection below the freezing level and enhancing convection aloft) is in agreement with previous idealized simulations of Morrison and Grabowski (2013, see Fig. 10 there) and RCE simulations in van den Heever et al. (2011) and Sheffield et al. (2015). Together with our interpretation of the observed impact of ship emissions on convection over major shipping lines (see discussion section 6 in GM20), simulations in Morrison and Grabowski (2013), van den Heever et al. (2011), and Sheffield et al. (2015) suggest that the “more convection” rather than “stronger convection” is the appropriate paradigm for the impact of pollution on convection–environment interactions.
Acknowledgments
The authors acknowledge partial supported from the U.S. DOE ASR Grants DE-SC0016476, DE-SC0020104, and DE-SC0020118. NCAR is sponsored by the National Science Foundation.
APPENDIX
Supersaturation and Quasi-Equilibrium Supersaturation
Figure A1 shows results of idealized calculations in which Eq. (A1) is solved over a depth of approximately 4 km assuming the updraft accelerates from 2 m s−1 at the initial height (zero in the figure) to about 20 m s−1 at 4 km. That takes about 6 min. Solid lines in the figure show solutions of Eq. (A1) and dashed lines show the quasi-equilibrium saturation calculated from the velocity at a given height, that is, as A1wτ. There are three sets of lines, each starting at S = 0.1%, for three phase relaxation time values. For τ = 1 s (giving a quasi-equilibrium supersaturation of 0.1% for w = 2 m s−1), the two lines are indistinguishable and the supersaturation at 4 km reaches 1%. For τ = 10 s, the differences are small but noticeable in the figure, and the supersaturation at 4 km reaches 10%. For τ increasing linearly in time from 1 s at the initial height to 21 s at 4 km, the differences are still relatively small, 19% for the solution from Eq. (A1) versus 21% for the quasi-equilibrium supersaturation at 4 km.
Solutions of the idealized supersaturation calculations (solid lines) and the diagnostic quasi-equilibrium supersaturation calculated when applying the local updraft velocity (dashed lines). See text for details.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0315.1
There are some similarities between the idealized calculations above and the dynamic model results presented in Fig. 4 of FK21. For instance, the quasi-equilibrium supersaturation calculated locally is typically larger than the one predicted by the model. The differences are much larger in Fig. 4 of FK21, and this arguably comes from many factors affecting the cloud model that are excluded from simple considerations above (e.g., entrainment). However, we are worried about the way the quasi-equilibrium supersaturation is calculated in FK21 and compared with model simulations. The key issue is with the droplet growth equation that FK21 use. The droplet growth equation is not presented in their appendix, but if the quasi-equilibrium supersaturation is calculated in the same way as in Pinsky et al. (2013), then this may result in some discrepancy. The phase relaxation formula (4) in Pinsky et al. (2013) is simpler than the formula applied in Politovich and Cooper (1988) because of the simplified droplet growth equation. Although the values calculated by two formulations are similar, differences up to 50% can exist (K. Chandrakar 2020, personal communication). The two formulations can be unified by applying the so-called modified water vapor diffusivity; see (11) in Kumar et al. (2013) or the appendix in Chandrakar et al. (2020, manuscript submitted to J. Atmos. Sci.). The key point is that one has to apply exactly the same droplet growth formula in the phase relaxation time calculation (and thus in the quasi-equilibrium supersaturation calculation) as used in the numerical model. We think this may not be the case with results presented in FK21.
For the dynamic model simulations, Fig. A2 shows a comparison between the model-predicted supersaturation and the quasi-equilibrium supersaturation at 3 km height and at hour 6 from the GM20 simulations, that is, part of the buoyancy plot shown in Fig. 5 of GM20. Overall, there is an agreement between the two, although some differences do exist. This is consistent with weak “warm invigoration” seen in these simulations.
Supersaturation predicted by the model vs the quasi-equilibrium supersaturation for GM20 simulations. Results are from simulations assuming (left) PRIS and (right) ADCN conditions. Data for hour 6 at 3 km height.
Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0315.1
Finally, an additional issue concerns the way supersaturation is calculated and used to obtain the condensation rate. Although solving the Lagrangian supersaturation equation in a parcel framework (as in the calculations shown in Fig. A1) is straightforward, it is nontrivial in Eulerian dynamical models. Specifically, diagnosing supersaturation from the advected temperature (or a temperature-like variable) and water vapor mixing ratio fields can generate large supersaturation errors and it leads to a “push–pull” problem whereby time step–dependent supersaturations are generated after advection in an updraft and then depleted by condensation (if the microphysics is calculated after advection, as in WRF). See section 3e in Hall (1980) for additional discussion. This leads to ambiguity in interpreting the supersaturation output from the model depending on when it is output during the time step. In GM20 as well as previous studies using our two-moment scheme, the problem is mitigated using the approach of Grabowski and Morrison (2008) and Morrison and Grabowski (2008a). In this approach, we separately advect the absolute supersaturation (water vapor mixing ratio minus the saturation mixing ratio) and apply a quasi-analytic solution to the supersaturation equation to obtain the condensation/evaporation rate. Further adjustment of the temperature and water vapor fields via condensation/evaporation is then done to ensure consistency with the predicted supersaturation field. As seen in Fig. A2, the supersaturation calculated using this method in the GM20 simulations shows some differences with the quasi-equilibrium supersaturation, but overall the two are fairly similar. This similarity is also consistent with the parcel calculations shown in Fig. A1. FK21 apply a much different method for evolving the supersaturation, and they seemingly produce larger differences between the actual supersaturation and quasi-equilibrium value than in our simulations (see Fig. A2). However, caution should be exercised in drawing general conclusions because FK21 simulated a different case study. As we suggest in section 6, using the same simplified modeling framework (and including piggybacking) would allow a rigorous comparison of our scheme and that of FK21. This could facilitate an understanding of the effects of using different approaches for calculating supersaturation, as well as differences in invigoration produced by the schemes more generally.
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