The POLDER-1 instrument was able to measure aerosol and cloud properties for eight months in 1996–1997. We use these observational data for aerosol concentration (the aerosol index), cloud optical thickness, and cloud droplet effective radius to establish statistical relationships among these parameters in order to analyze the first and second aerosol indirect effects. We also evaluate the representation of these effects as parameterized in the Laboratoire de Météorologie Dynamique–Zoom (LMDZ) general circulation model. We find a decrease in cloud top droplet radius with increasing aerosol index in both the model and the observations. Our results are only slightly changed if the analysis is done at fixed cloud liquid water path (LWP) instead of considering all LWP conditions. We also find a positive correlation between aerosol index and cloud liquid water path, which is particularly pronounced over the Northern Hemisphere midlatitudes. This may be interpreted as observational evidence for the second aerosol indirect effect on a large scale. The model-simulated relationship agrees well with that derived from POLDER data. Model simulations show a rather small change in the two relationships if preindustrial rather than present-day aerosol distributions are used. However, when entirely switching off the second aerosol indirect effect in our model, we find a much steeper slope than we do when including it.

Parameterisations of fractional cloudiness in large-scale atmospheric models rely on information about the subgrid-scale variablity of the total water specific humidity, qt , provided in form of a probability density function (PDF). In this contribution, four different approaches to evaluate such total-water PDFs are discussed: (i) Satellite spectroradiometers with high spatial resolution allow to construct at the scale of model grid boxes a histogram, and subsequently to derive the moments of the PDF, of the vertical integral of qt . This can be compared to the same quantity diagnosed from the model parameterisation. Although the vertical integral mostly focuses on the boundary layer, and involves issues in grid-boxes with orographic variability, it allowed nevertheless in the example presented to pinpoint deficiencies of a model parameterisation. (ii) Assuming a simple PDF shape and saturation within clouds, the simple “critical relative humidity” metric can be derived from infrared sounders and/or cloud lidar in combination with reanalysis data with a vertical resolution. It allows to evaluate the underlying PDF of any cloud scheme, but is sensitive to the assumptions. (iii) Supersites with a combination of ground-based lidar, radar and microwave data provide high-resolution high-quality reference data. In a “virtual reality” framework, we showed, however, that it is difficult to evaluate higher moments of a spatial PDF with this temporally-varying data. (iv) From a hierarchy of models from general circulation models to direct numerical simulations, we find that the variance of the qt follows a power-law scaling with an exponent of about -2. This information is very useful to improve the parameterisations.