UTH, i.e. the relative humidity with respect to water, in a layer between approximately 200 and 500 hPa, was obtained from the microwave humidity sounder (MHS; Bonsignori, 2007) on board the MetOp-A satellite for 60∘ S to 60∘ N. The ascending node was used, crossing the Equator northward at 21:30 local solar time. A microwave method developed by Buehler et al. (2008) enabled us to detect relative humidities also in the areas of anvil clouds.

The daily rainfall product, 3B42, from the Tropical Rainfall Measuring Mission (TRMM) multi-satellite analysis (Huffman et al., 2007) was used in this study. These data cover the globe from 50∘ S to 50∘ N and are provided on a 0.25∘ × 0.25∘ grid. The TRMM daily rainfall product consists of satellite and in situ measurements during a 24 h time period starting at 22:30 UTC of the previous day (in our study region approximately 08:30 local solar time).

AOD has in general been considered a moderate proxy of cloud condensation nuclei (CCN; Andreae, 2009). However, it should be noted that AOD does not provide information on aerosol type, vertical profile of the aerosols or hygroscopic growth of the aerosol particles. We used AOD from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on board the Terra satellite, which crosses the Equator southward at 10:30 local solar time (Remer et al., 2005). MOD08_D3 collection 5 level 3 global daily 1∘ × 1∘ data of the effective optical depth average ocean mean at 550 nm was used in most parts of the study, as well optical depth land and ocean mean in global analysis. MODIS level 3 products are obtained from level 2 swaths along the flight, with 10 km resolution for AOD and uncertainty of ±0.03 ± 0.05 × AOD over ocean. A satellite instrument cannot retrieve AOD below clouds, and in level 2 data the pixels adjacent to a cloud are also removed from the AOD product to avoid possible cloud contamination of the data. However, as the 1∘ × 1∘ level 3 data are produced from the 10 km-resolution level 2 data, it is possible to obtain AOD and cloud properties for the same 1∘ × 1∘ grid cell when this cell is partly cloudy (Fig. 2).

Cirrus clouds may contaminate the AOD values obtained from MODIS (Sun et al., 2011; Wollner et al., 2014; Huang et al., 2011). In our study region, MODIS AOD increased almost linearly with the increasing cirrus fraction (cf), obtained also from MOD08_D3 (Figs. 3 and 4). This may partly be due to a microphysical effect of aerosols, as more extensive cirrus anvils have been observed in association with higher AOD (Koren et al., 2005, 2010; Fan et al., 2013, and as shown schematically in Fig. 1a and b). However, AOD data contamination due to sub-visual cirrus is also possible (Sun et al., 2011; Wollner et al., 2014; Huang et al., 2011).

We removed data with cirrus fraction larger than 0.9 and used linear regression for cirrus fractions between 0.1 and 0.9 to remove the cirrus dependence from the AOD data to minimise the possible AOD data contamination (as explained in Fig. 4). However, by doing so, we also removed any possible microphysical effect of aerosols on cirrus anvils and subsequently may have underestimated the aerosol effect on UTH. Therefore, we also report results without the cirrus correction in Table 1. It should be noted that the applied cirrus correction is designed only to assure that our results are not contaminated by sub-visual cirrus; it is not, therefore, a general method to be applied in all satellite data.

For sensitivity tests (Table 2), a linear regression for the cirrus fractions between 0.1 and 0.9 was applied with a fit of AOD = 0.1486 × cf + 0.2535 and root mean square error of 0.3690 (cirrus correction version 2). The grid cells with a cirrus fraction larger than 0.9 were excluded from the analysis. For global data a similar cirrus correction as explained in Fig. 4 was applied, with a linear fit to global data of all seasons in 2007–2013: AOD = 0.072 × cf + 0.100. The cirrus correction may not be geographically or seasonally homogeneous, but for simplicity we applied the same correction to all grid cells in the global analysis.

We investigated the effect of aerosols on UTH in the maritime region east of China (25–45∘ N, 120–149∘ E). This area was chosen because of the advection of anthropogenic aerosols from the continent to this region and the frequent occurrence of convection (Fig. 5). We analysed data from days with precipitation for June, July and August in 2007–2013. Only data from the summer period were considered because during the other seasons, the advective wind speeds are much higher so that the 11 h time difference between the AOD and UTH measurements could have resulted in these two quantities being determined from totally different air masses.

We used measurements of AOD preceding the measurements of UTH by 11 h to better allow convection and microphysical changes, including sublimation of ice, to occur between the AOD and UTH measurements. Eleven hours may not be long enough to allow the sublimation of all ice associated with the large ice anvils produced in deep convection but a longer time lag could potentially lead to problems due to the horizontal advection of air. AOD was obtained from the Terra satellite crossing the Equator southward at 10:30 local solar time and UTH from the MetOp-A satellite crossing the Equator northward at 21:30 local solar time.

All data were linearly interpolated to the same 1∘ × 1∘ grid. The UTH data were binned according to daily precipitation in the same 1∘ × 1∘ grid. The applied data were restricted to cases when the daily precipitation was more than 1 mm. We use the limit of 1 mm to exclude cases without any deep convection from the study. For each grid point, ΔUTH was calculated as ΔUTH = median{UTH[AOD ≥ median(AOD)]} - median{UTH[AOD < median(AOD)]} for each precipitation bin, and an average was then calculated over the precipitation bins. Median(AOD) is the median of all AOD data in the study region for precipitation values of more than 1 mm day-1. For global analysis median(AOD) is the median of AOD in each grid box. The 90 % confidence interval of the mean was calculated as ±1.725 × SD/√N, where SD is the standard deviation of the N=21 monthly median values, which were assumed to be independent of each other. For global analysis, a two-sided t test was conducted over the monthly medians and only values significant at the 10 % level are shown. A logarithmic fit was calculated for the binned mean values in Fig. 6a, excluding the first data point. The obtained fit is UTH = 45.5015 + 1.3680 × ln(AOD).

The sensitivity of the radiative transfer to perturbations in the UTH was tested by using the libRadtran radiative transfer code (Mayer and Kylling, 2005). Reference soundings for the tropical atmosphere (Dunion, 2011) were used. We added 1, 2, 5 and 10 %RH to the 500–200 hPa layer of the reference soundings of tropical moist (TM) and midlatitude dry (MLD) air. The outgoing longwave flux at the top of the atmosphere was integrated over the 4–50 µm wavelength band using the DISORT radiative transfer equation solver (Stamnes et al., 1988) and the correlated k-method by Fu and Liou (1992). The radiative effects were calculated only for the longwave region, as the shortwave effect was estimated to be minor. Stratospheric adjustment was not taken into account.

We found that UTH increased with increasing values of AOD for AOD higher than about 0.08 (Fig. 6a). From a logarithmic fit to these values, the UTH increase associated with the AOD increase, for example from 0.1 to 0.6, was observed to be 2.5 % RH. An UTH increase was not visible with very high amounts of precipitation (Fig. 7), presumably due to enhanced wet scavenging of aerosols. In particular, earlier strong precipitation may result in larger UTH occurring together with smaller AOD, which then masks the microphysical effect of aerosols on UTH (Quaas et al., 2010; Grandey et al., 2013). Overall, wet scavenging associated with both earlier and simultaneous precipitation masks the effect of aerosols on UTH; therefore our results may underestimate the true effect.

The median AOD over the study region was 0.18 for precipitation values of more than 1 mm day-1. We selected this median to represent the limit between high and low AOD. The mean UTH difference between these two AOD categories (ΔUTH) was 2.2 ± 1.5 % RH (90 % confidence interval, see Sect. 2.4) for precipitation values of more than 1 mm day-1 (Fig. 6b, see also Fig. 8). Without applying the cirrus correction, which removes part of the real microphysical effect, the corresponding UTH difference was much higher, 5.8 ± 1.4 % RH (Table 1). Without the precipitation binning, or with only a few bins, a larger mean difference in UTH between cases with high and low AOD was obtained (Fig. 9). UTH also increased less as a function of AOD in Fig. 6a when averaged over 10 precipitation bins than when the median values without precipitation binning were used. The fact that precipitation binning decreases the obtained ΔUTH may be at least partly due to the removal of invigoration effects of aerosols on precipitation.

We tested the sensitivity of the results by varying the limit between high and low AOD and by averaging AOD over 5∘ × 5∘. We also varied the time lag between AOD and UTH measurements, and the time span over which the precipitation was taken, up to 2 days. Furthermore, different aerosol products were tested. In general, a higher UTH was observed with a higher value of AOD. However, the magnitude of ΔUTH depended on the specific choices (Table 2).

Causalities in satellite studies of aerosol–cloud interactions have been questioned because of meteorological covariation and aerosol humidification (Quaas et al., 2010; Grandey et al., 2013). For example, aerosol particles have been noted to swell in humid conditions leading to higher AOD even though the number of cloud condensation nuclei does not change (e.g. Quaas et al., 2010; Grandey et al., 2013; Twohy et al., 2009). Such effects may then cause correlations between AOD and cloud properties.

Although precipitation binning should alleviate these problems, we repeated our analysis by binning the data according to different meteorological variables from ERA-Interim reanalysis data (Dee et al., 2011) in addition to binning it by the amount of precipitation. Surface parameters and 550 hPa vertical velocity in pressure coordinates at 00:00 UTC (approximately 10:00 local solar time) were used at 1∘ × 1∘ resolution (Fig. 10).

If meteorological covariation or humidification explained our results, binning by meteorological variables should significantly decrease the observed UTH difference between the high and low values of AOD. For cases with non-extreme values for meteorological variables (i.e. boxes 2 to 5 in Fig. 10), the results were practically the same as with binning only by precipitation. With extreme values of some meteorological parameters (the lowest mean sea level pressure, the highest 2 m relative humidity and the largest pressure increase from the previous day), the results showed a weaker or even a negative relation between AOD and UTH. However, those values were likely associated with current or recent passage of low pressure systems, where the wet scavenging associated with significant amount of earlier precipitation may dominate the results. We conclude that meteorological covariation and humidification were not the reason for the observed association between UTH and AOD. This strongly suggests a causal relationship between aerosols and UTH.

Outgoing longwave radiation is sensitive to the upper tropospheric water vapour concentration (Held and Soden, 2000). Water vapour is a greenhouse gas that mainly affects climate by absorbing outgoing longwave radiation. To balance the decrease in outgoing longwave radiation that results from increased UTH, an increase in surface and lower atmospheric temperature is required which acts to increase the outgoing longwave radiation.

To quantify these effects, radiative transfer calculations (see Sect. 2.5) were conducted for two reference soundings of TM and MLD air. The results show that a 1 % RH increase in the UTH of moist tropical air causes a local positive radiative effect of 0.25 W m-2 (0.39 W m-2 for dry air, see Table 3). In dry air the impact is larger as the fractional increase in water vapour concentration for a fixed increase in RH is larger in dry air (Held and Soden, 2000).

The observed summertime increase of 2.2 ± 1.5 % RH in UTH (5.8 ± 1.4 % RH without removal of AOD dependence on cirrus fraction) due to aerosols corresponds to the radiative effect of +0.5 ± 0.4 W m-2 (+1.4 ± 0.3 W m-2, interpolated from Table 3) in tropical moist air. The real radiative effect of this phenomenon may be even larger than these values, since the effect of wet scavenging may partially obscure the microphysical effects of aerosols on UTH in our study region.