Experience weather forecasters called this situation a "dirty ridge" whenever a lot of low clouds (such as stratocumulus) are present but NWP models fail to forecast them and instead predict sunny conditions. This situation often happens.
Thorne, Peter W., Philip Brohan, Holly A. Titchner, Mark P. McCarthy, Steve C. Sherwood, Thomas C. Peterson, Leopold Haimberger, et al. 2011. ‘A Quantification of Uncertainties in Historical Tropical Tropospheric Temperature Trends from Radiosondes’. Journal of Geophysical Research: Atmospheres 116 (D12): n/a – n/a. doi:10.1029/2010JD015487. The process that they are missing is that the behaviour of the greenhouse effect in the Boundary Layer is non linear and so the Schwarzschild equation of radiative transfer is not appropriate in that region of the atmosphere.
If the NWP models are failing to forecast "dirty ridges" then "all models may be missing some fundamental climate process such as a nonlinear response to
I expect that not all models fails in this respect, but low clouds are problematic for many models due to several reasons. One reason may be that models often lack sufficient vertical resolution to capture the sharp gradients at the cloud top that is a necessary feature for the physics involved; the clouds are also often shallow. Another is that the model's description of moist processes, cloud/radiation interaction or boundary layer turbulence may be inadequate.
One problem is that the presence (or not) of stratocumulus is due to a balance between resolved-scale motions (subsidence in the high-pressure ridge) and motions that in a model are parameterized (turbulent mixing). If the mixing is too weak compared to the subsidence there will not be any clouds; if the mixing is too strong the clouds will be to thick.
Prior responses are one reason why (in the USA and likely other places and met-services) model output statistics are used to run numerical model output through various regression equations that can "see" the potential for production of stratocu within ridge situations. These statistical predictions do not always 'catch' all of the events but do tend to at least 'suggest' to an operational forecaster to look over the weather balloon report from the prior day or night from upstream and at the location.
From operational forecasters I've worked with over time they usually mention that they make use of boundary layer profiles, mixing height/depth, and low level moisture (and sometimes soil moisture or state of the ground, snow/ice-pack) that produce low level instability and convective processes/mixing in the presence of a surface ridge with larger scale subsidence present (a capping inversion of sorts). The end result is typically a layer of stratocu that forms a short time after sunrise and that only begins to clear at sunset in spite of a 'mostly sunny' forecast for the day.
Someone once said: If stratocumulus did not exist, life of weather forecaster would be much easier. But life of atmospheric scientist would be less challenging :)
Thank you very much to all of you for your answers.
Very true(!); in fact one major reason for going after low clouds in my PhD-thesis a long time ago, was my experiences as an aviation meteorology forecaster, dealing with stratus, stratocumulus and fog. And it has kept me busy...