Complex interplay of sulfate aerosols and meteorology conditions on precipitation and latent heat vertical structure

The Beijing-Tianjin-Hebei (BTH) region, recognized as China’s capital economic zone, is rapidly urbanizing and industrializing^1,2,3. The primary source of atmospheric sulfate is the oxidation of SO₂, which mainly emanates from human activities, industrial processes, and the combustion of fossil fuels⁴. As a scattering aerosol, sulfate reflects incident solar radiation into space, reducing the amount of solar radiation that reaches the surface and thereby affecting the radiation balance—an effect known as the radiative effect of aerosols^5,6. This radiative effect cools the surface and results in a more stable atmosphere, potentially suppressing precipitation or altering the ___location of precipitation zones^7,8,9. It is worth to mention that absorbing aerosols, instead of scattering aerosols, when located below clouds, can cool the surface, heat the atmosphere, and increase the instability of atmosphere to enhance convection and precipitation^5,6. Furthermore, hygroscopic sulfate aerosols, serving as effective cloud condensation nuclei (CCN), participate in cloud microphysical processes, influence the phase state of hydrometeors, affect cloud radiative properties, lifetime, and alter the total amount and vertical distribution of latent heat (LH) release—known as the indirect effect of aerosols^2,10,11,12.

Under the condition of given cloud water content, when the atmospheric CCN increases due to the presence of a large number of aerosols, it will intensify the competition for water vapor among cloud droplets, reduce the particle size of cloud droplets¹³, and inhibit the process of particle collision-coalescence and riming processes¹⁴, so that weak precipitation is not easy to occur, and the life cycle of the cloud is prolonged. More liquid particles are lifted to higher levels to form more ice-phase hydrometeors formations, releasing additional LH, enhancing the development of convection, and intensifying precipitation^12,15. However, it has also been found that under conditions of abundant cloud water content, the increase in the amount of collectible cloud water offsets and outweighs the competition between small droplets^16,17.

Aerosol indirect effects are subject to atmospheric dynamic conditions because meteorological factors impact both aerosol and precipitation systems^6,15,18. These indirect effects involve the interplay of macro and microscale processes, encompassing complex mechanisms and significant uncertainties in the influencing processes, making the isolation and quantification of aerosol effects on precipitation extremely challenging due to the intricate interactions between cloud microphysics, radiation, and atmospheric dynamics^19,20. For example, Sun et al²¹. found that the effect of aerosols on convective precipitation top heights (PTH) is a boomerang-shape, from invigoration to suppression, resulting from competition between heating by condensation and freezing and cooling by evaporation. Convective available potential energy (CAPE) reflects the overall structural characteristics of the atmosphere²² and is a key variable representing atmospheric dynamical conditions, widely used in aerosol-cloud-precipitation interaction studies to quantify the capacity to produce convective clouds and precipitation^11,16,18. Zhu et al.¹⁸ quantitatively assessed the influence of CAPE and dust aerosol optical depth (AOD) on precipitation top temperatures (PTT) using satellite observations and characterizing atmospheric dynamical conditions with CAPE.

A recent review by Zhao et al.⁵ provided comprehensive observational evidences and underlying mechanisms of aerosol’s effects on precipitation over the past several decades. For instance, Wang et al.² used numerical experiments to find that the aerosol-cloud interaction of sulfate led to an increase in the CCN at a supersaturation of 0.1% at 850 hPa by approximately 30%, and the vertically integrated cloud droplet number concentrations increased accordingly. This reduced the effective radius of cloud droplets below 850 hPa by 4%, and increased the total liquid water path by 11%, which caused a decline in the radiation reaching the surface, consequently cooling the atmosphere. Such changes diminished the thermal contrast between land and sea, resulting in a decreased total precipitation rate in the southern part of the East Asian monsoon region. Zhou et al.²³ identified that sulfate aerosols in the North China Plain and the Tibetan Plateau increased cloud droplet number concentrations, reduced cloud droplet size, inhibited the warm rain process, and transported more cloud droplets above the 0 °C isotherm. This led to a heightened release of LH during the mixed-phase process and thereby strengthened cumulus cloud updrafts, increasing precipitation. Meanwhile, Guo et al.²⁴ determined that in the Pearl River Delta region, polluted conditions with high PM₁₀ concentrations correlated with weak wind shear and comparatively humid meteorological conditions, presenting convective precipitation radar reflectivity that was deeper and stronger than that under clean conditions. Zhang et al.²⁵ corroborated through model simulations that anthropogenic aerosol emissions in Southern China augmented radar reflectivity in the midlevel of convective systems and elevated convective cores to higher altitudes. Clavner et al.¹⁶ simulated a supercell thunderstorm and discovered that in the moist convective region, the increase in cloud water available for collection superseded the decreased efficiency of aerosol-induced precipitation from smaller droplets, thereby enhancing precipitation conversion. Higher aerosol concentrations also intensified convective updrafts through aerosol thermodynamic effects, further increasing precipitation. Conversely, for stratiform precipitation, a greater aerosol concentration led to diminished cloud water in the stratiform-anvil and weakened the efficiency of small particle collision-coalescence and riming processes, ultimately reducing precipitation.

Previous studies have largely centered on the impact of anthropogenic aerosols in China on total precipitation rate changes^2,25 and precipitation timing (start time, peak time, and duration)¹⁰, detecting instances where sulfate aerosols both invigorated^23,24 and suppressed^2,10,11 precipitation. Studies on the effect of aerosols on the vertical structure of precipitation have been conducted since the launch of the first space-born precipitation radar (Rosenfeld et al.²⁶) and received increasing attention in recent years. Li et al.^27,28,29,30 systematically studied the effect of dust aerosols on the vertical structure of clouds and precipitation. For example, Li and Min²⁷ analyzed the variation of rain rates with altitude and found that the effect of dust aerosols on cloud and precipitation systems is highly dependent on rain type. Sun et al.²¹ found that aerosols have different effects on rain rates in different layers of convective precipitation. Zhu et al.¹⁸ found that aerosols enhanced the growth rate of precipitation particles in the middle atmospheric layers (with a temperature of between −5 and +2 °C). However, a comprehensive mechanism to explain the observed phenomena remains elusive. Furthermore, the potential influence of sulfate aerosols on the vertical structure of precipitation and the associated release of LH has not been extensively investigated. To address this, our study analyzed precipitation characteristics from 2014 to 2021 in the BTH region (35-43°N, 110-120°E) under intense sulfate-dominated summer aerosol loadings and comparatively pristine conditions, focusing particularly on vertical structure parameters such as PTT, the vertical growth rate of precipitating particles, and LH. We quantitatively estimated the effects of sulfate aerosols and CAPE on the vertical structure of precipitation using the mathematical approach proposed by Zhu et al.¹⁸.

Coupling between aerosol and meteorological conditions

The spatial distribution of Aerosol Optical Depth (AOD) derived from MERRA-2 during summers (2014–2021) was analyzed. Figure 1 illustrates that on polluted days (Fig. 1b), the study area experiences substantial aerosol pollution, with the total AOD (TAOD) exceeding 1.0 across extensive areas. Concurrently, the spatial distribution of sulfate AOD showed a strong correlation with TAOD, as the average AOD to TAOD ratio is 0.8. This indicates that the atmospheric aerosols in the BTH region during summer are predominantly sulfate. Conversely, on defined pristine days, both TAOD and sulfate AOD in the study region are significantly lower compared to polluted days.

a, b Total aerosol optical depth. c, d Sulfate aerosol optical depth. a–h Wind fields (U&V, m/s) and (e, f) specific humidity (q, g/kg) at 850 hPa. g, h Convective available potential energy (CAPE, J/kg). Where (a, c, e, g) for pristine days, (b, d, f, h) for polluted days.

Full size image

The study region harbors numerous sulfate aerosol sources, such as industry, power plants, and transport, resulting in high atmospheric aerosol loading. This pollution is exacerbated by southerly winds, which transport heavier pollution and water vapor from the ocean, especially in the southern part of the BTH region (Fig. 1b, d). The northward movement of polluted air masses at lower altitudes is hindered by the Taihang Mountains to the northwest, impeding diffusion and favoring the formation of secondary atmospheric aerosols. Conversely, when northern winds prevail, the concentration of sulfate aerosols is diluted due to lighter pollution to the northwest. Additionally, the relatively dry and cold air brought by northwestern/northern winds generally lowers atmospheric hydrostatic energy and stability.

We further analyzed the key averaged atmospheric circulation parameters at low (850 hPa, Fig. 1), middle (500 hPa, Supplementary Fig. 1), and upper (300 hPa, Supplementary Fig. 2) atmospheric layers. During precipitation on polluted days, data showed relatively stronger vertical velocity (W, Pa/s), increased specific humidity (q, g/kg), stronger southeastern winds, and higher temperatures (T, °C). Summarizing these dynamic conditions, the mean CAPE on polluted days is found to be stronger than on pristine days. The correlation coefficient between TAOD and CAPE is 0.13 (p < 0.05). Such conditions are conducive to the vertical growth of convection. In essence, there is a noteworthy coupling between high sulfate concentrations and the prevailing meteorological conditions.

Effect of CAPE and sulfate aerosols on the vertical structure of precipitation and LH

The vertical structure of precipitation mirrors microphysical and thermodynamic processes within precipitation clouds, predominantly governed by the strength of updraft^31,32 and influenced to some extent by aerosols^18,24,27,33. To analyze the impact of meteorological conditions on precipitation, we utilized CAPE as an overall indicator. We compared mean precipitation rate profiles under polluted and pristine conditions with classified CAPE (Fig. 2, based on probability distribution analysis in Supplementary Fig. 3) and PTT (Supplementary Fig. 4) to control for dynamic-related variations. Within a given CAPE range (Fig. 2), the onset temperature (and corresponding altitude) for precipitation in polluted (red curves) conditions is higher (lower) than in pristine (blue curves) conditions, and the rain rate in pristine conditions surpasses that in polluted conditions in the upper layer (above the −5 °C isotherm). This difference is statistically significant at the 95% confidence level (Fig. 2). However, around the −5 °C to 0 °C layer, the precipitation rate under polluted conditions accelerates more rapidly, aligning with model simulations^16,25. Aerosols may enhance the collision-coalescence process of precipitation particles in the mixing layer¹⁸, which makes the precipitation particles grow rapidly. Sulfate aerosols consume large amounts of water vapor in the mixing layer, weakening the vertical transport of water vapor to the upper levels³⁴, so the rain rate is weaker than the pristine conditions at the upper layer, and results in an overall decrease (warming) of precipitation top height (precipitation top temperature). Upon reaching the +2 °C to +5 °C isotherms, precipitation rates in polluted samples significantly outpace those in pristine ones (Fig. 2 and Supplementary Fig. 4). In the low layer, precipitation particle growth is gradual, and the final near-surface rain rate (NSRR) in polluted conditions markedly exceeds that in pristine conditions.

a, g, m Stratiform precipitation. d, j, p Convective precipitation. The shading indicates the standard deviation. And t-test for the differences between polluted and pristine conditions of (c, i, o) stratiform precipitation and (f, l, r) convective precipitation (the dashed line indicates the 95% confidence level at 100 degrees of freedom). The subplots take the logarithm of (b, h, n) stratiform precipitation rate and (e, k, q) convective precipitation rate for the upper levels and focus on the height/temperature of precipitation onset.

Full size image

The fluctuations observed in precipitation microstructure also bear upon LH (Fig. 3 and Supplementary Fig. 5). For stratiform (convective) precipitation, the peak normalized LH (LH_max) under polluted conditions is 0.8 (0.6) K/mm—higher than the pristine condition maximums of 0.5 (0.5) K/mm—and the altitude of LH_max is released at 4.9 (5.8) km, lower than the 5.1 (6.6) km in pristine conditions (Fig. 3). These differences are statistically significant at the 95% confidence level (Fig. 3b, d). Furthermore, at altitudes above 6 km, the LH is marginally higher in pristine than in polluted conditions. Contoured Frequency by Altitude Diagrams (CFADs) of LH (Supplementary Fig. 5) under polluted conditions display an increased occurrence of stronger LH near the 5 km altitude, heightened instances of stronger cooling absorption at lower altitudes, and a reduction in weaker LH occurrences at higher altitudes. The microphysical process of aerosol-cloud interaction discussed above leads to associated energy transfer variations in the vertical direction. At the layers around 5 km, the precipitation formation process in the polluted conditions was enhanced by aerosol thus producing a faster growth rate (Figs. 2, 6) and stronger rain rate. Such enhancement releases a larger amount of LH in the middle layers than that in pristine conditions. Meanwhile, this process promotes the vertical development of non-raining clouds^12,15, and the non-raining cloud top heights under polluted conditions move to higher altitudes compared to that under pristine conditions (Supplementary Fig. 6). On the other hand, the quick assumption of water at the middle layer weakened the precipitation formation at the upper layer thus the LH release is also depressed. Therefore, it was observed the LH at the upper layer under polluted conditions is weaker than that in pristine conditions. In the low layers, the increase in the occurrence of strong cooling in polluted conditions may be due to stronger evaporation processes of precipitation particles caused by higher temperatures in polluted conditions²¹ (Supplementary Figs. 1i, 2i).

a Stratiform precipitation. c Convective precipitation. The t-test result of the difference between pristine and polluted conditions for (b) stratiform precipitation, (d) convective precipitation (the dashed line indicates the 95% confidence level at 100 degrees of freedom).

Full size image

Effect of Sulfate aerosols on microphysical processes

To discern the influence of sulfate aerosols on the vertical structure of precipitation, we examined the two-dimensional probability distributions of liquid cloud radius and liquid cloud water path (LWP) under pristine and polluted conditions (Fig. 4, see Supplementary Information 6 for details). In the presence of given LWP values, the occurrence of smaller liquid cloud particles decreases, and that of larger ones increases under polluted conditions (Fig. 4c). This indicates a significant increase in the effective radius of liquid cloud particles due to sulfate aerosols.

Two-dimensional probability distributions of liquid cloud radius and LWP (g m⁻²) based on MOD08_D3 and MYD08_D3 derived for (a) pristine condition, (b) polluted conditions, and (c) the differences between polluted and pristine conditions (polluted - pristine). Where the number in each grid in (a, b) represents the sample size.

Full size image

The role of sulfate aerosols was further elucidated by comparing CloudSat-observed liquid water content (LWC) on pristine and polluted days. According to CloudSat data (Fig. 5), polluted samples (solid curves) display higher LWC between altitudes of 4 and 7 km, providing a larger quantity of particles that bolster the collision-coalescence process—consistent with model simulation results¹⁶. Essentially, sulfate aerosols function as CCN, leading to rapid growth and increased radius of cloud droplets in a highly humid ambient environment (Figs. 1f, 5a, and Supplementary Figs. 1d, 2d), enhancing particle collision-coalescence efficiency. In addition, the LWC and effective radius of non-raining clouds in polluted conditions increased, confirming that aerosols invigorate cloud development and that cloud tops develop higher (Supplementary Fig. 6).

a CloudSat observed LWC (mg/m³) corresponding to pristine (dashed curve) and polluted (solid curve) days, and (b) t-test results for the differences between polluted and pristine conditions (the dashed line indicates the 95% confidence level at 100 degrees of freedom).

Full size image

To quantify the growth rate of precipitating particles across various atmospheric layers, we calculated the linear regression slope of the logarithm of precipitation rate to temperature (i.e., dlogR/dT), following the methodology of Li et al.³¹. Figure 6 (the horizontal coordinate is the precipitation top temperatures (PTT) associate with the Slope, not the temperature range itself), S7, and S8 compare slopes above the −10 °C isotherm (SlopeA), between the −5 °C and 2 °C isotherms (SlopeB), and below the 2 °C isotherm (SlopeC) for deep convective and stratiform precipitation under pristine and polluted conditions at upper, middle, and low atmospheric levels, respectively.

For a given PTTs, differences in the (a, b) SlopeA, (e, f) SlopeB, and (i, j) SlopeC for (a, e, i) stratiform precipitation and (b, f, j) convective precipitation under pristine (dotted curves) and polluted (solid curves) conditions. The t-test significance for the differences of (c, d) SlopeA, (g, h) SlopeB, and (k, l) SlopeC between pristine and polluted conditions (red (black) line indicates the 95% (99%) confidence level at 100 degrees of freedom).

Full size image

In the middle layer, SlopeB associated with a given PTT is notably higher under polluted conditions (Fig. 6e, f and Supplementary Figs. 7f, 8f), which indicates rapid particle growth within the mixed layer. This difference is statistically significant at the 99% confidence level (Fig. 6g, h). The increased LWC at altitudes of 4-7 km under polluted circumstances (Fig. 5) likewise boosts collision-coalescence chances, hastening particle growth¹⁶. In the upper atmospheric levels, pristine conditions exhibit marginally higher SlopeA compared to their polluted counterparts (Fig. 6a, b and Supplementary Figs. 7c, 8c). This could be due to the depletion of water vapor in the middle layer by sulfate aerosols, restricting the transport of vapor upstairs and dampening particle deposition efficiency, thereby slowing growth³⁴.

At low levels, SlopeC under polluted conditions is lower than under pristine conditions (Fig. 6i, j and Supplementary Figs. 7i, 8i), predominantly negative for stratiform precipitation (Fig. 6i), largely indicative of raindrop evaporation or breakup, this is consistent with the results of Sun et al.²¹. For deep convective precipitation, a slight upsurge in precipitation persists at these low levels due to cloud droplet coalescence. However, the SlopeC is subdued for convective precipitation in polluted conditions, suggesting inhibited droplet coalescence. One plausible explanation for this could be the higher temperatures in polluted conditions (Supplementary Figs. 1i, 2i), facilitating raindrop evaporation and in line with model predictions²⁵. Another potential reason, as proposed by Zhao et al.¹¹, might be the intense competition for water vapor among the numerous sulfate aerosols acting as CCN, reducing cloud droplet size, and thereby hindering lower-level precipitation.

Effect of CAPE and Sulfate aerosols on PTT

The preceding analysis makes it evident that sulfate aerosols, acting as additional CCN, significantly alter cloud microphysical processes (Figs. 4, 6), which subsequently impacts the macroscopic characteristics of precipitation. The Precipitation Top Temperature (PTT) in relation to the Near-Surface Rain Rate (NSRR) is fundamentally influenced by dynamic (e.g., CAPE) and aerosol conditions (ref. ¹⁸). Adopting the method used by Zhu et al.¹⁸, we delved into the PTT-NSRR relationship for pristine and polluted situations and assessed the sensitivity of PTT to both CAPE and AOD (refer to Methods for details).

Satellite observations showcase the PTT-NSRR relationship under pristine conditions—indicative of minimal aerosol impacts—as displayed in Supplementary Fig. 9a, b. Here, cloud dynamics represented by CAPE appears to be the overriding factor. It is observable that at comparable NSRR levels, PTTs with robust CAPE (black line, > 300 J/kg) are 4–6 °C colder than those associated with feeble CAPE (gray line, < 100 J/kg). These disparities pass the t-test with 99% (95%) confidence for stratiform (convective) precipitation (Supplementary Fig. 9d, e).

To examine the CAPE-induced variations of PTT from theoretical point of view, we simulated the dependences of PTT on CAPE in the BTH region during August 2017 under aerosol-free assumption using both the microphysical parameterization schemes of Thompson³⁵ and the Morrison³⁶ with the Weather Research and Forecasting (WRF)³⁷ cloud-resolving model. The detailed configuration of the WRF simulation is detailed in Methods. The WRF simulation result further confirms the satellite observed CAPE influence on PTT. As shown in Supplementary Fig. 9c, WRF simulations affirm a linear PTT-NSRR relationship and corroborate that at consistent NSRR levels, PTTs under higher CAPE conditions (> 300 J/kg) are cooler than those under weaker CAPE ( < 100 J/kg), with a discrepancy of approximately 5–7 °C according to the Thompson scheme and 1–5 °C per the Morrison scheme. These differences also fulfill the t-test criterion at 99% (95%) confidence (Supplementary Fig. 9f, g). This supports the understanding that robust dynamic conditions are conducive to cooler PTTs.

Contrariwise, on polluted days marked by relatively stronger CAPE (refer to Fig. 1h), satellite observations depict a noticeable 3–4 °C elevation in PTT for equal NSRRs relative to pristine days (Fig. 7a, b)—a contrast ratified by the t-test at a 99% confidence level (Fig. 7d, e). This phenomenon arises due to the aerosols’ (primarily sulfates) role as CCN heightening collision-coalescence efficiency in the mixed layer, which expedites particulate growth¹⁶. Such advancements result in increased PTT, a warming influence that negates and supersedes the cooling effect of CAPE, leading to a net warmer PTT under polluted versus pristine conditions.

Satellite observed PTT-NSRR relationships for (a) stratiform precipitation and (b) convective precipitation under pristine (black dashed curves), polluted (black solid curves), and CAPE-corrected conditions (red solid curves). (c) WRF simulated PTT-NSRR relationships corresponding to the two microphysical parameterizations of Morrison (dashed curve) and Thompson (point curve). The t-test result of the difference between pristine and polluted conditions for (d) stratiform precipitation, (e) convective precipitation (red (black) line indicates the 95% (99%) confidence level at 100 degrees of freedom).

Full size image

Isolating and quantifying the dynamic and aerosol influences on PTT-NSRR, satellite observations convey that for each 100 J/kg dip in CAPE, the commencement PTT of stratiform and convective precipitation escalates by 0.74 °C and 0.31 °C, respectively (Supplementary Fig. 10a, b). Correspondingly, WRF model simulations indicate increases of 0.99 °C for the Thompson scheme and 0.66 °C for the Morrison scheme with each 100 J/kg CAPE reduction (Supplementary Fig. 10c, d). The alignment of these satellite-derived sensitivities with cloud-resolving model outcomes lends credence to the estimated PTT responsiveness to CAPE as both plausible and dependable. Furthermore, with every unit uptick in atmospheric AOD, PTT for convective and stratiform precipitation ascends by 5.43 °C and 5.01 °C, respectively. Modifying the polluted condition CAPE to mirror that in pristine states yielded a corrected PTT-NSRR association for polluted conditions (red curves in Fig. 7a, b, refer to Methods for details), signifying that, under uniform dynamic circumstances, sulfate aerosols can indeed elevate precipitation top temperatures.

This study’s extensive satellite data analysis spanning eight years has uncovered that in the Beijing-Tianjin-Hebei (BTH) area, hygroscopic aerosols, by acting as cloud condensation nuclei (CCN), enhance the collision-coalescence process within mixed-phase clouds. This aerosol-induced enhancement occurs particularly in environments with high cloud water content, leading to larger cloud droplet sizes and the accelerated growth of precipitation particles. Sulfate aerosols consume large amounts of water vapor in the mixing layer, weakening the vertical transport of water vapor to the upper levels³⁵ thus decreased the precipitation top height. Consequently, this process raises the Precipitation Top Temperature (PTT) as shown in Fig. 8. The increase in PTT brought about by aerosols unexpectedly overrides the cooling effect typically associated with Convective Available Potential Energy (CAPE).

In polluted cloud, sulfate aerosol acting as cloud condensation nuclei (CCN), amplify the collision-coalescence process within the mixed layer amid high cloud water content and propelling rapid precipitation particle growth, depleting a large amounts of water vapor in the mixed layer, weakening the vertical transport of water vapor to the upper levels thus decreased the precipitation top height (PTH). This effect overrides the lifting of the PTH by the strong thermodynamic conditions.

Full size image

In addition, it was found that precipitation in polluted conditions releases additional LH in the low and middle layers, promoting vertical cloud development and higher non-raining cloud top heights compared to pristine conditions. Aerosols enhance or suppress the particle collision-coalescence process, echoing the dynamics observed in Clavner et al.¹⁶ simulation of super-hurricane precipitation, where the outcome hinges on the degree to which precipitating particles can accumulate cloud water particles.

The response of PTT to CAPE has been corroborated using Weather Research and Forecasting (WRF) model simulations over one month, aligning with the satellite observations. However, these simulations did not factor in aerosol impacts on precipitation, nor did they validate PTT’s sensitivity to Aerosol Optical Depth (AOD). Future modeling efforts are called to expand spatial coverage and extend simulation durations to fully interrogate aerosols’ influence on precipitation patterns, building on preliminary findings such as those presented by Zhang et al.²⁵.

It should be noted that there are uncertainties in the MERRA-2 aerosol properties. For instance, the global mean sulfate (total) AOD for MERRA-2 is approximately 15% (9%) higher than that of the AeroCom multimodel^38,39. A sensitivity test assuming a 15% reduction in sulfate AOD and a 9% reduction in total AOD for MERRA-2 was conducted to reinvestigate the associated impact on the PTT-NSRR relationship (Supplementary Fig. 11). It was found the general conclusion remains unchanged with the increase of 16% (19%) in \(\frac{\partial {PT}{T}_{0}}{\partial {AOD}}\) (sensitivity of PTT₀ to AOD) for stratiform (convective) precipitation. Such an effect will not significantly change our conclusion. Since there is no in-situ measurements of AOD over long periods and at large scales, and current satellite remote sensed AOD is only available at clear sky and has weak information of aerosol type, it is a feasible way to use MERRA-2 AOD which is global, long-lasting, and available under all sky with aerosol type information. In addition, aerosols are strongly coupled to dynamic and thermodynamic conditions^40,41. It is difficult to disentangle the covariation of clouds due to aerosols and meteorology conditions^5,42. In this study, we attempt to isolate these two effects on precipitation top temperature (PTT, an indicator of precipitation vertical development) from three aspects. We first control for consistent thermodynamic conditions in pristine and polluted conditions by classifying CAPEs (Fig. 2). Then, we use observations and model simulations to quantify the dependence of PTT on CAPE (Supplementary Figs. 9, 10). Third, we subtracted the effect of CAPE on PTT from the observed covariances of PTT due to both meteorology conditions and aerosol conditions (Supplementary Fig. 13).

CAPE was selected as the single parameter for representing the meteorology condition based on the following investigations: 1) CAPE is a synthetic parameter of dynamic and thermodynamic conditions. After constraining the CAPE range, the statistics show that other considered dynamic and thermodynamic parameters (e.g., RH at 500/750 hPa, wind shear, and boundary layer height) are largely constrained (with variations less than 10% mostly, Supplementary Tables 1, 2 and Supplementary Fig. 12). 2) The partial correlation coefficients⁴³ of other dynamic parameters with PTT are weaker than that of CAPE (Supplementary Table 3 and Supplementary Fig. 13). 3) When CAPE was not constrained, the dependence of PTT on considered dynamic and thermodynamic parameters was unstable and dispersed (Supplementary Figs. 14, 15), and was not suitable to be used as a constraint parameter of atmospheric dynamic conditions. 4) Sensitivity tests show that expressing the change in PTT as a function of CAPE and AOD captures 76% (70%) of the variations from the PTT of convective (stratiform) precipitation.

Satellite observations and reanalysis of datasets

Our research incorporates precipitation profiles data from the Global Precipitation Measurement (GPM) Mission Dual-frequency Precipitation Radar (DPR). Based on the quantified relationship between rain rate and radar reflectivity (i.e. Z-R relationship) and comprehensive treatments of the path integrated attenuation, precipitation rate profiles were retrieved at a vertical resolution of 125 m and horizontal resolution at 5 km⁴⁴. Because the low-level rain rate profile detected by DPR is affected by smeared surface echo⁴⁵, all profiles are terminated around 20 °C. The height of precipitation top was defined as the beginning altitude of the first (from up to down) three consecutive bins with DPR detectable rain echo. And the associated temperature in the environment is defined as the precipitation top temperature (PTT). The classification of convective and stratiform precipitation is based on the methodologies in previous literature^31,45,46. In addition, the LH at different altitudes were derived based on GPM DPR measurements using the Vertical Profile Heating profile algorithm of Li et al.⁴⁶. This study mainly focuses on cold rains with PTT < 0 °C. For warm rain with PTT > 0°C, their PTT was artificially confined below the freezing layer making it difficult to study its dependence on aerosols and CAPE. Meanwhile, the sample size is small (about 10%). Therefore, the associated analysis of warm rain process is not included in the main text. The discussion related to warm rain is detailed in the Supplementary Information (Supplementary Figs. 16–18).

To examine the vertical structure changes of non-precipitating clouds under varying aerosol loadings, CloudSat’s Cloud Profiling Radar (CPR) data were sourced, which offer insights into the liquid water content (LWC) at a fine vertical resolution⁴⁷. These datasets are complemented with the Moderate Resolution Imaging Spectroradiometer (MODIS) instruments on board the Aqua and Terra satellites for daily assessments of cloud physical properties like cloud radius and water path³⁴.

Aerosol characterization is enriched by the second Modern-Era Retrospective analysis for Research and Applications (MERRA-2), which provides a breakdown of Aerosol Optical Depth (AOD) into various constituents⁴⁸. This study devised a method to link the aerosol data to observed precipitation, categorizing certain days as “polluted” or “pristine” based on specific AOD thresholds. For each GPM DPR detected raining pixel, the MERRA-2 AODs averaged from all grids 0.5° surrounded and within one hour in advance to satellite overpass time is assigned to it. For a given observation day, if the mean sulfate AOD from all raining pixels is larger than 0.65 (a threshold of 75% of the cumulative probability of mean sulfate AOD), then the day was defined as a polluted day. All samples on that day were defined as polluted rains. If the mean total TAOD is less than 0.35 (a threshold of 25% of the cumulative probability of mean total AOD), the day was defined as pristine day, and all samples on that day were defined as pristine rains.

To account for atmospheric thermodynamic conditions, we utilized the ERA5 reanalysis data, allowing for an analysis of various meteorological parameters at different atmospheric levels⁴⁹. By averaging this thermodynamic information corresponding to the satellite overpass times during designated pristine or polluted days, we were able to construct a reference atmospheric state within which to frame our precipitation observations.

Weather Research and Forecast (WRF) model simulations

This study utilized the WRF model version 4.0³⁷ for simulating precipitation within the BTH region in August 2017. The simulation spanned from 00UTC on July 31, 2017, to 00UTC on August 31, 2017, delivering output at 6 h intervals. Model spin-up effects were mitigated by discarding results from the first 24 h. The grid setup (Supplementary Fig. 19 and Supplementary Table 4) employed a dual grid nesting scheme with outer and inner resolutions of 12 km and 4 km, respectively. The model top was set at 50 hPa, with time resolutions for the outer and inner model simulations set at 60 s and 20 s correspondingly.

The physical scheme configurations selected for inclusion in the model included the RRTMG long-wave radiation⁵⁰, RRTMG short-wave radiation scheme⁵⁰, Mellor-Yamada-Janjic (Eta) TKE scheme⁵¹, and the unified Noah land surface scheme⁵². The Tiedtke convective parameterization⁵³ was applied in the outer ___domain, while turned off in the inner one. The two differing microphysical schemes employed for comparison were the Thompson scheme³⁵ and the Morrison scheme³⁶.

The meteorological driving fields for the model’s initial fields and boundary conditions were sourced from the NCEP Climate Forecast System Version 2 (CFSV2) 6-hourly Products⁵⁴ and NCEP FNL operational global analysis data⁵⁵.

We calculate the precipitation rate \({{Rr}}_{x}\) (unit: mm/hr) as:

Where \(x\) refers to three kinds of precipitation particles, namely rain (r), snow (s) and graupel (g), \({\nu }_{x}\) is the terminal velocity (unit: m/s),\({q}_{x}\) is the mixing ratio (unit: kg/kg), ρ is the density of air (unit: kg/m³), ρ′ is the density of water (unit: kg/m³). Then the total precipitation rate is the sum of the three, i.e.

The PTT in the model results is defined as the lowest temperature where the vertical precipitation rate is greater than or equal to 0.5 mm/hr.

The sensitivity of PTT to CAPE and AOD

It was parameterized PTT as a linear function of NSRR (Zhu et al.¹⁸):

Where K is the linear regression slope, and PTT₀ is the intercept when NSRR equals to zero. Physically, it means the height of precipitation onset.

The variations of PTT₀ to CAPE and AOD are parameterized as:

Therefore, the sensitivity of PTT₀ to aerosol \(\frac{\partial {PT}{T}_{0}}{\partial {AOD}}\) can be separated from the overall satellite observations by removing the sensitivity of PTT₀ to CAPE \(\,\frac{\partial {PT}{T}_{0}}{\partial {CAPE}}\):

The sensitivity of \(\frac{\partial {PT}{T}_{0}}{\partial {CAPE}}\) was calculated using satellited observed and WRF simulated pristine precipitation samples without aerosol-induced variation. About 70% pristine samples were randomly selected and sorted into 6 bins of CAPE. The PTT₀ in each bin was determined by the PTT-NSRR relationship of Eq. (3), and the sensitivity of \(\frac{\partial {PT}{T}_{0}}{\partial {CAPE}}\) can be estimated using the six determined values of PTT₀. To determine the variation of \(\frac{\partial {PT}{T}_{0}}{\partial {CAPE}}\) of this estimation, we repeated this experiment 40 times with different randomly selected samples. All the results are shown in Supplementary Fig. 10.

Substituting the estimated \(\frac{\partial {PT}{T}_{0}}{\partial {CAPE}}\), the mean values of \(\varDelta {PT}{T}_{0}\), \(\varDelta {AOD}\), and \(\varDelta {CAPE}\) between polluted and pristine precipitation samples into the Eq. (5), the sensitivity of PTT₀ to AOD \(\frac{\partial {PT}{T}_{0}}{\partial {AOD}}\) was obtained.

Finally, we correct the CAPE-induced variation of PTT in polluted conditions as:

Where ΔCAPE is the difference of mean CAPE between polluted and pristine days.