Linking Atmospheric Cloud Radiative Effects and Tropical Precipitation

Studies in recent decades have demonstrated a robust relationship between tropical precipitation and column relative humidity (CRH). The present study identifies a similar relationship between CRH and the atmospheric cloud radiative effect (ACRE) calculated from satellite observations. Like precipitation, the ACRE begins to increase rapidly when CRH exceeds a critical value near 70%. We show that the ACRE can be estimated from CRH, similar to the way that CRH has been used to estimate precipitation. Our method reproduces the annual mean spatial structure of the ACRE in the tropics, and skillfully estimates the mean ACRE on monthly and daily time scales in six regions of the tropics. We propose that the exponential dependence of precipitation on CRH may be partially explained by cloud‐longwave feedbacks, which facilitate a shift from convective to stratiform conditions.

Recent observational and modeling studies have shown a strong link between atmospheric humidity and tropical precipitation (Ahmed & Schumacher, 2015;Bretherton et al., 2004;Inoue & Back, 2015;Powell, 2019;Masunaga & L'Ecuyer, 2014;Raymond, 2000;Raymond & Zeng, 2005;Raymond et al., 2009;Rushley et al., 2018;Wolding et al., 2020;Zeng, 1999). Bretherton et al. (2004) showed that tropical precipitation can be modeled as an exponential function of column relative humidity (CRH, defined as the ratio between the water vapor path and saturation water vapor path), and this relationship has been used in many applications including theoretical studies of the MJO (see Rushley et al., 2018, and references therein). More recently, Ahmed and Schumacher (2015) used observations from the DYNAMO field campaign (Yoneyama et al., 2013) and satellite estimates of precipitation to show that the rapid increase of precipitation in humid regions is due to stratiform rather than convective rainfall. Furthermore, they found that the area covered by stratiform precipitation accounts for much of the nonlinearity in the precipitation-humidity relationship, while the area covered by convective precipitation is only a weakly nonlinear function of the CRH.
In this study, we suggest a link between longwave-cloud feedbacks and the observed relationship between tropical precipitation and CRH. Section 2 describes the data. In Section 3, the ACRE is shown to be a strong function of the CRH, while Section 4 demonstrates that CRH may be used to estimate the tropical ACRE on annual mean, monthly, and daily time scales. Conclusions are discussed in Section 5.

Data and Methods
Top of atmosphere and surface fluxes of longwave and shortwave radiation come from the CERES SYN1deg Ed4a product (Doelling et al., 2013, hereafter CERES). CERES data were downloaded on a 1° × 1° grid. Daily mean radiative fluxes were used to calculate the CRE as the difference between full-sky and clear-sky fluxes. The CRE was calculated at the top of the atmosphere and at the surface, and the ACRE was calculated as the difference between the two.
Reanalysis fields of temperature and specific humidity were downloaded from ERA5 (Hersbach et al., 2018(Hersbach et al., , 2020 at a temporal resolution of 6 h on the native 0.25° × 0.25° grid. The CRH was calculated as follows: where q* is the saturation vapor pressure. The ERA5 data were averaged to daily means and to the coarser 1° × 1° CERES grid. Both data sources span the same 19-years period from January 1, 2001 to December 31, 2019. Analysis was restricted to the tropical belt ranging from 30°S to 30°N. The analysis was repeated for six subset regions which represent the Indo-Pacific warm pool, Pacific ITCZ, south Pacific convergence zone (hereafter SPCZ), Pacific cold tongue, Atlantic ITCZ, and Atlantic cold tongue.
In addition, we utilize precipitation rates from the TRMM Multisatellite Precipitation Analysis (3B42 product, Huffman et al., 2016) to show climatology and to reproduce the exponential relationship between CRH and precipitation.

ACRE Binned by CRH
The tropical band ranging from 30°S to 30°N is characterized by wide distributions of precipitation and humidity (Figures 1a and 1b). This includes regions of warm SSTs with enhanced convection and regions of cool SSTs with suppressed convection. Land surface covers ∼25% of this belt, which introduces additional complexity.
We now perform a binning analysis, following the method used in previous studies. The area-weighted average TRMM precipitation rate was found for each CRH bin of width 2% ranging from 0% to 100%. The NEEDHAM AND RANDALL 10.1029/2021GL094004 interquartile range was also found as a measure of the spread of precipitation in each bin. This procedure was repeated for the net, longwave, and shortwave ACRE over the entire tropical belt with results shown in Figure 1c through Figure 1f.
The net ACRE ( Figure 1d) is negative or zero when the CRH is small, due to longwave and shortwave contributions which mostly offset (Figures 1e and 1f). When the CRH becomes large the longwave component changes sign and begins to increase. The shortwave component also increases, but at a slower rate. The combination of both terms leads to a rapid increase of the net ACRE above a value of about 70% CRH. This behavior is evocative of the dependence of precipitation on CRH ( Figure 1c). As proposed in Section 5, this NEEDHAM AND RANDALL 10.1029/2021GL094004 3 of 9 similarity may be the result of cloud-longwave feedbacks in humid regions of the tropics that promote a shift from convective to stratiform precipitation.
A comparison of Figures 1e and 1f shows that the ACRE is largely determined by the longwave component, consistent with previous studies (Allan, 2011;Slingo & Slingo, 1988). Similar curves result when this analysis is repeated for the six regions shown in Figure 1a even though the regions have markedly different distributions of CRH (Figures S1 and S2 of supporting information). The only obvious difference is due to the influence of marine stratus clouds in the cold tongue regions (Klein & Hartmann, 1993;Schneider et al., 2019;Voigt et al., 2021), which have a large shortwave ACRE and tend to be found in regions with low CRH.

Estimating ACRE From CRH
The interquartile range in Figure 1d is small, which indicates little spread in the distribution of the ACRE at a given CRH. This suggests a tight relationship between CRH and ACRE. In this section, we investigate whether the CRH can be used to estimate ACRE, similar to how it has been used to estimate precipitation. To estimate ACRE, the daily mean CRH at a grid cell at a particular timestep was mapped onto the mean curves in Figures 1e and 1f to calculate the longwave and shortwave contributions. These fields were then combined to estimate the net ACRE at each grid cell.  Figure 2a shows the annual mean ACRE calculated from the observed CERES fluxes. The ACRE is positive over the Indo-Pacific, SPCZ, and ITCZ regions due to the absorption of longwave radiation by convective clouds and organized systems. In the cold-tongue regions, the reflection of sunlight by marine stratus clouds reduces the shortwave radiation that would have otherwise been absorbed, which leads to a negative ACRE. The cooling albedo effect is smaller than the warming greenhouse effect so that the ACRE averaged over the 30°S to 30°N belt is 15.193 W m −2 . In Figure 2b the time mean of the estimated ACRE is shown. The estimated ACRE largely reproduces the same spatial structure as the observed ACRE, which includes large positive values over the Indo-Pacific, SPCZ, and ITCZ regions, and negative values in the marine stratus regions. The annual mean ACRE estimated from CRH is 15.203 W m −2 ; a difference of about 0.01 W m −2 .

Time Mean Estimation of ACRE
The difference between the estimated and observed ACRE is shown in Figure 2c. The estimation method has a positive bias in the east Pacific relative to the west Pacific. This is partially due to the longwave CRE at the top of the atmosphere (not shown) and is consistent with Kubar et al. (2007) who found that the temperature of high tropical clouds in the east Pacific was about 5 K warmer compared to similar clouds in the west Pacific. In addition, the estimation method gives negative errors over land compared to mostly positive errors over oceans. We emphasize that this is merely the first attempt to estimate the ACRE from CRH and a more optimal method likely exists, perhaps one that includes the cloud ice path to separate low and high clouds. Figure 3 compares the time series of the observed and estimated monthly mean ACRE anomaly for each of the six regions outlined in Figure 1a. Anomalies were calculated as the monthly average ACRE over the region minus the time mean ACRE for that region for each month, which effectively removes the seasonal cycle. The agreement between the observed and estimated ACRE was evaluated using Pearson's R 2 correlation, which is shown in the lower left-hand corner of each panel.

Accuracy of the Estimation on Shorter Time Scales
The Indo-Pacific, SPCZ, and both ITCZ regions each show a high degree of correlation, with R 2 greater than 0.6 or 0.7. The estimation method is able to account for the large peaks in magnitude in the warm pool and pacific ITCZ regions in 2010 and 2015-2016 which are likely associated with the strong El Niño events of those years (National Weather Service, 2020, see Figure S3 through Figure S6 from supporting information). The correlation is slightly lower for the cold tongue regions, with R 2 equal to 0.56 and 0.515 in the Pacific and Atlantic, respectively. Together, this indicates that more than 50% of the variance of the ACRE on monthly time scales is due to variations in CRH for each of these regions (Bony et al., 2004).
The R 2 correlations for the monthly mean time series are recorded in Table S1, alongside the R 2 correlations for the daily mean time series, which were constructed similarly. On daily time scales the agreement is lower than monthly time scales, although the correlation is still greater than 0.6 in the warm pool, and greater than 0.4 in all regions except for the Pacific cold tongue. From this, it appears that the CRH method shows some skill at estimating the ACRE even on time scales shorter than a month.

Discussion and Conclusions
We have shown that the ACRE estimated from 1° × 1° daily mean satellite observations varies with the CRH in a way that is similar to the well-documented relationship between precipitation and CRH. Both are small when the CRH is small, and begin to increase rapidly when the CRH exceeds a value near 70%. In addition, we have shown that the CRH can be used to estimate the ACRE similar to how it has been used to estimate precipitation.
Why do ACRE and precipitation behave so similarly when analyzed using the CRH? We believe that this is more than just a coincidence and that the dependence of precipitation on CRH is linked to the ACRE through cloud-longwave feedbacks which have been recently discussed in reference to organized tropical systems.
Complementary to this study, Needham and Randall (2021) discuss this type of feedback in the context of a set of idealized simulations. They found that ACRE in extremely humid regions is powerful enough to change the sign of the net radiation tendency, which leads to a convergence of energy into the atmosphere. The net heating drives stratiform ascent which lifts water vapor and moistens the troposphere (Ahmed & Schumacher, 2015;Chikira, 2014;Jenney et al., 2020). In addition, they found that ACRE is independent of SST at a particular CRH in the idealized simulations, consistent with the results presented here. They also performed a set of simulations in which the radiative heating rate is homogenized over the domain. In this case, the CRH distribution is narrower and the extreme precipitation is less frequent, as shown in Figure 4. The homogenized radiation also leads to a reduction in the dry static energy export out of humid regions.
NEEDHAM AND RANDALL 10.1029/2021GL094004 6 of 9 The cloud-longwave feedback described by Needham and Randall (2021) may contribute to the well-documented relationship between precipitation and CRH. Humid regions promote the formation of clouds, which in turn absorb radiation. The ACRE leads to net heating which drives stratiform ascent. This ascent favors a shift from isolated convection to more organized systems that are characterized by stratiform precipitation. As discussed by Ahmed and Schumacher (2015), the area covered by stratiform precipitation increases exponentially at high CRH and appears to be responsible for the characteristic pickup of the precipitation rate above the critical threshold. Future studies should focus on investigating this hypothesis through mechanism-denial experiments which may help to demonstrate causality in the relationship we have shown between ACRE and tropical precipitation.

Data Availability Statement
All of the data used in this study are freely available online. ERA5 reanalysis data were downloaded from the ECMWF Copernicus Climate Data Store (CDS), accessible at https://cds.climate.copernicus.eu/ keyword search "ERA5." CERES SYN1deg_Ed4a data were obtained from the NASA Langley Research Center Atmospheric Science Data Center (ASDC), accessible at https://ceres.larc.nasa.gov/data/ under the heading "Synoptic TOA and surface fluxes and clouds (SYN)." TRMM data were downloaded from the Goddard Earth Sciences Data and Information Services Center (GES DISC), accessible at https://disc.gsfc.nasa.gov/ keyword search "TRMM_3B42." Figure 4. Probability density functions of column radiative humidity (a) and precipitation rate (b) for two simulations analyzed by Needham and Randall (2021). "Control" refers to a simulation performed with a fixed SST of 300 K, no rotation, and uniform insolation. "RADAVG" is identical to Control, except for radiative heating, which is globally averaged at each timestep. Originally from Needham and Randall (2021).