Possible links between cloud optical depth and effective radius in remote sensing observations

The theoretical relationship between cloud optical depth and effective radius is examined. The relationship between cloud optical depth and effective radius is shown to depend on (a) the relative variability of droplet concentration, cloud depth, mixing and precipitation, and (b) the correlation between the two most important parameters, namely cloud depth and droplet concentration. It is possible to obtain positive, negative or zero correlation between optical depth and effective radius for different values of (a) and (b). Of all these parameters, mixing appears to be the least important. If clouds are not affected by precipitation, negative correlations between optical depth and effective radius (the expected signature of the first indirect aerosol effect) can be caused by a small spread in cloud depths relative to that in droplet concentration, or (more importantly) by a positive correlation between droplet concentration and cloud depth. Precipitation tends to reduce the correlation between optical depth and effective radius, because one of the main effects of precipitation is to increase the spread in droplet effective radius. If the effect of increases in aerosols is a reduction in precipitation, our results indicate that the correlation coefficient between optical depth and effective radius should increase, an effect that should be most clearly visible over the ocean. These findings illustrate the complexity of the physical processes that underpin the linkage of optical depth and effective radius.