## 1 Introduction  
One of the outstanding issues regarding the earth's energy balance and subsequent climate budget are the indirect effects that aerosols have on cloud radiative properties. In particular, Twomey [1] increased aerosol loading results in higher concentration of cloud condensation nuclei that ultimately lead to increased cloud droplet number concentration and smaller effective cloud droplets, which have to be compared, however, for constant liquid water paths. Unlike direct cloud effects on the climate, the aerosol-cloud indirect interactions are very hard to measure directly from satellites, since simultaneous aerosol loadings (especially below cloud base) and cloud properties such as COD and/or R\({}_{\rm eff}\) are not possible and therefore efforts at quantifying these effects are limited to statistical trends studied over large domains. However, because of the difficulties of more direct approaches, extensive satellite studies of aerosol-cloud indirect effect have been pursued and supported by significant improvement in multispectral satellite sensors onboard polar orbiting satellites. For example, regional measurements and resultant cloud products from MODIS (MODerate resolution Imaging Spectroradiometer) were used [2] together with aerosol properties estimated from the MODIS (e.g., aerosol optical depth product) to ascertain statistical relationships between appropriate aerosol and cloud parameters which include Cloud Top Temperature and Pressure, Cloud Droplet Number Concentration (CDNC), Total Cloud Fraction, Water Path, Cloud Droplet Effective Radius (R\({}_{\rm eff}\)), Cloud Optical Thickness (COD), Cloud Condensation Nuclei (CCN) and Aerosol Optical Thickness (AOT). In this study, it was found that on average large regions are laden with fluctuating correlations between cloud and aerosol metrics, which average to zero as might be expected. However, with appropriate binning of the data by Liquid Water Path (LWP) and with ancillary data provided by ISCCP (International Satellite Cloud Climatology Project) to ascertain regions of dominant cloud type (stratus or convective clouds), an inverse relationship between the size of the water droplet (effective radius) and column cloud droplet number concentration, cloud optical thickness (reflectivity) and cloud fraction emerged. These relationships were connected to the aerosol properties through an observed inverse correlation between aerosols and droplet radii in support of the general Aerosol Indirect Effect (AIE). However, the story is not so clear-cut. For example, both modeling and observation studies have suggested possible correlations between AOT and LWP [3, 4]. Nevertheless, the analysis of the data showed significant differences between low AOT (\(\tau_{\rm a}<0.1\)) and higher AOT (\(\tau_{\rm a}>0.1\)). In particular, for low AOT, a strong positive correlation was observed, but for high AOT, a strong negative correlation between aerosols and water path was observed. Further studies showed even more complex behavior. To remove some of the inherent difficulties in simultaneous cloud/aerosol retrieval, aircraft measurements of large scale marine stratocumulus decks showed significant correlation between CDNC and accumulation mode number concentration (AMNC) below cloud base [5] reporting a regression result of \(0.72\pm 0.04\) with an \(R^{2}\) of 0.90. This result indicates that a satellite remote sensing approach to quantifying CDNC should be a reasonable proxy for aerosol signatures (at least for relatively clean maritime conditions) in exploring aerosol-cloud interaction. To utilize this observation, [PERSON] _et al._[6], studied the correlations between LWP and CDNC for warm water clouds (cloud-top temperature \(>\) 273 K, optical thickness \(1<\tau_{\mathrm{c}}<15\)). These results, however, revealed three distinct relationships between cloud liquid water path with aerosol changes: increasing, approximately constant, or decreasing as column CDNC increases, each occurring with nearly equal probability.